Whitehead groups of finite groups /:
This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1988.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
132. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area. |
| Beschreibung: | 1 online resource (349 pages) |
| Bibliographie: | Includes bibliographical references (pages 340-347) and index. |
| ISBN: | 9781107361355 1107361354 9780511600654 0511600658 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn839304956 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 130415s1988 enk ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d E7B |d IDEBK |d OCLCF |d YDXCP |d OCLCQ |d AGLDB |d OCLCQ |d HEBIS |d OCLCO |d UAB |d OCLCQ |d VTS |d OCLCA |d REC |d OCLCO |d STF |d AU@ |d OCLCO |d M8D |d OCLCO |d SFB |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO |d INARC |d OCLCL |d OCLCQ | ||
| 019 | |a 704520637 | ||
| 020 | |a 9781107361355 |q (electronic bk.) | ||
| 020 | |a 1107361354 |q (electronic bk.) | ||
| 020 | |a 9780511600654 |q (e-book) | ||
| 020 | |a 0511600658 |q (e-book) | ||
| 020 | |z 0521336465 | ||
| 020 | |z 9780521336468 | ||
| 035 | |a (OCoLC)839304956 |z (OCoLC)704520637 | ||
| 050 | 4 | |a QA171 |b .O44 1988eb | |
| 072 | 7 | |a MAT |x 014000 |2 bisacsh | |
| 082 | 7 | |a 512/.22 |2 22 | |
| 084 | |a PB 09 |2 blsrissc | ||
| 084 | |a *18-02 |2 msc | ||
| 084 | |a 16-02 |2 msc | ||
| 084 | |a 16E20 |2 msc | ||
| 084 | |a 16H05 |2 msc | ||
| 084 | |a 16S34 |2 msc | ||
| 084 | |a 18F25 |2 msc | ||
| 084 | |a 20-02 |2 msc | ||
| 084 | |a 20C05 |2 msc | ||
| 084 | |a 20D15 |2 msc | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Oliver, Robert, |d 1949- |1 https://id.oclc.org/worldcat/entity/E39PCjwxdQWcK8JPDmWvQBTMWC |0 http://id.loc.gov/authorities/names/n87843931 | |
| 245 | 1 | 0 | |a Whitehead groups of finite groups / |c Robert Oliver. |
| 260 | |a Cambridge [Cambridgeshire] ; |a New York : |b Cambridge University Press, |c 1988. | ||
| 300 | |a 1 online resource (349 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a London Mathematical Society lecture note series ; |v 132 | |
| 504 | |a Includes bibliographical references (pages 340-347) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area. | ||
| 505 | 0 | |a Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences | |
| 505 | 8 | |a 3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm | |
| 505 | 8 | |a 6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules | |
| 505 | 8 | |a 11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index | |
| 650 | 0 | |a Whitehead groups. |0 http://id.loc.gov/authorities/subjects/sh85146542 | |
| 650 | 0 | |a Finite groups. |0 http://id.loc.gov/authorities/subjects/sh85048354 | |
| 650 | 0 | |a Induction (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85065806 | |
| 650 | 6 | |a Groupes de Whitehead. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 6 | |a Induction (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Induction (Mathematics) |2 fast | |
| 650 | 7 | |a Whitehead groups |2 fast | |
| 650 | 7 | |a Whitehead-Gruppe |2 gnd |0 http://d-nb.info/gnd/4189790-0 | |
| 650 | 7 | |a Endliche Gruppe |2 gnd | |
| 650 | 7 | |a Teoria dos grupos. |2 larpcal | |
| 650 | 7 | |a Groupes finis. |2 ram | |
| 650 | 7 | |a Whitehead, Groupes de. |2 ram | |
| 650 | 7 | |a Induction (mathématiques) |2 ram | |
| 776 | 0 | 8 | |i Print version: |a Oliver, Robert, 1949- |t Whitehead groups of finite groups. |d Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1988 |z 0521336465 |w (DLC) 87027725 |w (OCoLC)16805916 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 132. |0 http://id.loc.gov/authorities/names/n42015587 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396 |3 Volltext | |
| 938 | |a Internet Archive |b INAR |n whiteheadgroupso0000oliv | ||
| 938 | |a ebrary |b EBRY |n ebr10441002 | ||
| 938 | |a EBSCOhost |b EBSC |n 552396 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis25154502 | ||
| 938 | |a YBP Library Services |b YANK |n 10407389 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn839304956 |
|---|---|
| _version_ | 1813903607364321280 |
| adam_text | |
| any_adam_object | |
| author | Oliver, Robert, 1949- |
| author_GND | http://id.loc.gov/authorities/names/n87843931 |
| author_facet | Oliver, Robert, 1949- |
| author_role | |
| author_sort | Oliver, Robert, 1949- |
| author_variant | r o ro |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171 .O44 1988eb |
| callnumber-search | QA171 .O44 1988eb |
| callnumber-sort | QA 3171 O44 41988EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences 3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm 6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules 11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index |
| ctrlnum | (OCoLC)839304956 |
| dewey-full | 512/.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.22 |
| dewey-search | 512/.22 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>06005cam a2200853 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn839304956</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">130415s1988 enk ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">E7B</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCF</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">HEBIS</subfield><subfield code="d">OCLCO</subfield><subfield code="d">UAB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">OCLCA</subfield><subfield code="d">REC</subfield><subfield code="d">OCLCO</subfield><subfield code="d">STF</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCO</subfield><subfield code="d">M8D</subfield><subfield code="d">OCLCO</subfield><subfield code="d">SFB</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">INARC</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">704520637</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781107361355</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1107361354</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780511600654</subfield><subfield code="q">(e-book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0511600658</subfield><subfield code="q">(e-book)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">0521336465</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9780521336468</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)839304956</subfield><subfield code="z">(OCoLC)704520637</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA171</subfield><subfield code="b">.O44 1988eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">014000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">512/.22</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">PB 09</subfield><subfield code="2">blsrissc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">*18-02</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16-02</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16E20</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16H05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">16S34</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">18F25</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">20-02</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">20C05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">20D15</subfield><subfield code="2">msc</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Oliver, Robert,</subfield><subfield code="d">1949-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjwxdQWcK8JPDmWvQBTMWC</subfield><subfield code="0">http://id.loc.gov/authorities/names/n87843931</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Whitehead groups of finite groups /</subfield><subfield code="c">Robert Oliver.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Cambridge [Cambridgeshire] ;</subfield><subfield code="a">New York :</subfield><subfield code="b">Cambridge University Press,</subfield><subfield code="c">1988.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (349 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">London Mathematical Society lecture note series ;</subfield><subfield code="v">132</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 340-347) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Whitehead groups.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85146542</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Finite groups.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85048354</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Induction (Mathematics)</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85065806</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Groupes de Whitehead.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Groupes finis.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Induction (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Group Theory.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finite groups</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Induction (Mathematics)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Whitehead groups</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Whitehead-Gruppe</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4189790-0</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Endliche Gruppe</subfield><subfield code="2">gnd</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Teoria dos grupos.</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Groupes finis.</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Whitehead, Groupes de.</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Induction (mathématiques)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Oliver, Robert, 1949-</subfield><subfield code="t">Whitehead groups of finite groups.</subfield><subfield code="d">Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1988</subfield><subfield code="z">0521336465</subfield><subfield code="w">(DLC) 87027725</subfield><subfield code="w">(OCoLC)16805916</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">London Mathematical Society lecture note series ;</subfield><subfield code="v">132.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n42015587</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">whiteheadgroupso0000oliv</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10441002</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">552396</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis25154502</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">10407389</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn839304956 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-25T16:21:22Z |
| institution | BVB |
| isbn | 9781107361355 1107361354 9780511600654 0511600658 |
| language | English |
| oclc_num | 839304956 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (349 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Oliver, Robert, 1949- https://id.oclc.org/worldcat/entity/E39PCjwxdQWcK8JPDmWvQBTMWC http://id.loc.gov/authorities/names/n87843931 Whitehead groups of finite groups / Robert Oliver. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1988. 1 online resource (349 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 132 Includes bibliographical references (pages 340-347) and index. Print version record. This book's aim is to make accessible techniques for studying Whitehead groups of finite groups, as well as a variety of related topics such as induction theory and p-adic logarithms. The author has included a lengthy introduction to set the scene for non-specialists who want an overview of the field, its history and its applications. The rest of the book consists of three parts: general theory, group rings of p-groups and general finite groups. The book will be welcomed by specialists in K- and L-theory and by algebraists in general as a state-of-the art survey of the area. Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences 3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm 6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules 11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index Whitehead groups. http://id.loc.gov/authorities/subjects/sh85146542 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Induction (Mathematics) http://id.loc.gov/authorities/subjects/sh85065806 Groupes de Whitehead. Groupes finis. Induction (Mathématiques) MATHEMATICS Group Theory. bisacsh Finite groups fast Induction (Mathematics) fast Whitehead groups fast Whitehead-Gruppe gnd http://d-nb.info/gnd/4189790-0 Endliche Gruppe gnd Teoria dos grupos. larpcal Groupes finis. ram Whitehead, Groupes de. ram Induction (mathématiques) ram Print version: Oliver, Robert, 1949- Whitehead groups of finite groups. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1988 0521336465 (DLC) 87027725 (OCoLC)16805916 London Mathematical Society lecture note series ; 132. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396 Volltext |
| spellingShingle | Oliver, Robert, 1949- Whitehead groups of finite groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Preface; List of notation; Contents; Introduction; Historical survey; Algorithms for describing Wh(G); Survey of computations; Part I General theory; Chapter 1. Basic algebraic background; 1a. Orders in semi simple algebras; 1b. P-adic completion; 1c. Semi local rings and the Jacobson radical; 1d. Bimodule-induced homomorphisms and Morita equivalence; Chapter 2. Structure theorems for Ki of orders; 2a. Applications of the reduced norm; 2b. Logarithmic and exponential maps in p-adic orders; Chapter 3. Continuous K2 and localization sequences 3a. Steinberg symbols in K2(R)3b. Continuous K2 of p-adic orders and algebras; 3c. Localization sequences for torsion in Whitehead groups; Chapter 4. The congruence subgroup problem; 4a. Symbols in K2 of p-adic fields; 4b. Continuous K2 of simple Qp-algebras; 4c. The calculation of C(Q[G]); Chapter 5 First applications of the congruence subgroup problem; 5a. Constructing and detecting elements in SKi: an example; 5b. Cl1(R[G]) and the complex representation ring; 5c. The standard involution on Whitehead groups; Chapter 6. The integral p-adic logarithm 6a. The integral logarithm for p-adic group rings6b. Variants of the integral logarithm; 6c. Logarithms defined on Kc2(ZP[G]); Part II Group rings of p-groups; Chapter 7. The torsion subgroup of Whitehead groups; Chapter 8. The p-adic quotient of SK1(Z[G]): p-groups; 8a. Detection of elements; 8b. Establishing upper bounds; 8c. Examples; Chapter 9. Cl1(Z[G]) for p-groups; Chapter 10. The torsion free part of Wh(G); Part III General finite groups; Chapter 11. A quick survey of induction theory; 11a. Induction properties for Mackey functors and Green modules 11b. Splitting p-local Mackey functorsChapter 12. The p-adic quotient of SK1(Z[G]): finite groups; Chapter 13. Cl1(Z[G]) for finite groups; 13a. Reduction to p-elementary groups; 13b. Reduction to p-groups; 13c. Splitting the inclusion Cl1(Z[G]) C SK1(Z[G]); Chapter 14. Examples; References; Index Whitehead groups. http://id.loc.gov/authorities/subjects/sh85146542 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Induction (Mathematics) http://id.loc.gov/authorities/subjects/sh85065806 Groupes de Whitehead. Groupes finis. Induction (Mathématiques) MATHEMATICS Group Theory. bisacsh Finite groups fast Induction (Mathematics) fast Whitehead groups fast Whitehead-Gruppe gnd http://d-nb.info/gnd/4189790-0 Endliche Gruppe gnd Teoria dos grupos. larpcal Groupes finis. ram Whitehead, Groupes de. ram Induction (mathématiques) ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85146542 http://id.loc.gov/authorities/subjects/sh85048354 http://id.loc.gov/authorities/subjects/sh85065806 http://d-nb.info/gnd/4189790-0 |
| title | Whitehead groups of finite groups / |
| title_auth | Whitehead groups of finite groups / |
| title_exact_search | Whitehead groups of finite groups / |
| title_full | Whitehead groups of finite groups / Robert Oliver. |
| title_fullStr | Whitehead groups of finite groups / Robert Oliver. |
| title_full_unstemmed | Whitehead groups of finite groups / Robert Oliver. |
| title_short | Whitehead groups of finite groups / |
| title_sort | whitehead groups of finite groups |
| topic | Whitehead groups. http://id.loc.gov/authorities/subjects/sh85146542 Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Induction (Mathematics) http://id.loc.gov/authorities/subjects/sh85065806 Groupes de Whitehead. Groupes finis. Induction (Mathématiques) MATHEMATICS Group Theory. bisacsh Finite groups fast Induction (Mathematics) fast Whitehead groups fast Whitehead-Gruppe gnd http://d-nb.info/gnd/4189790-0 Endliche Gruppe gnd Teoria dos grupos. larpcal Groupes finis. ram Whitehead, Groupes de. ram Induction (mathématiques) ram |
| topic_facet | Whitehead groups. Finite groups. Induction (Mathematics) Groupes de Whitehead. Groupes finis. Induction (Mathématiques) MATHEMATICS Group Theory. Finite groups Whitehead groups Whitehead-Gruppe Endliche Gruppe Teoria dos grupos. Whitehead, Groupes de. Induction (mathématiques) |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552396 |
| work_keys_str_mv | AT oliverrobert whiteheadgroupsoffinitegroups |