Skew linear groups /:
This book is concerned with subgroups of groups of the form GL(n, D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant dif...
Gespeichert in:
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
©1986.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
118. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book is concerned with subgroups of groups of the form GL(n, D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory, and algebraists and research students will find this an accessible account of the subject. |
| Beschreibung: | Includes indexes. |
| Beschreibung: | 1 online resource (253 pages) |
| Bibliographie: | Includes bibliographical references (pages 227-236) and indexes. |
| ISBN: | 9781107361379 1107361370 9780511600630 0511600631 1139881779 9781139881777 1107366283 9781107366282 1107371007 9781107371002 1107368626 9781107368620 1299404073 9781299404076 1107363829 9781107363823 |
| ISSN: | 0076-0052 ; |
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| 504 | |a Includes bibliographical references (pages 227-236) and indexes. | ||
| 500 | |a Includes indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book is concerned with subgroups of groups of the form GL(n, D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory, and algebraists and research students will find this an accessible account of the subject. | ||
| 505 | 0 | |a Cover; Title; Copyright; Contents; 1. BASIC CONCEPTS; 1.1 Irreducibility; 1.2 Absolute Irreducibility; 1.3 Unipotence; 1.4 Constructions; 2. FINITE AND LOCALLY FINITE GROUPS; 2.1 Finite Subgroups of Division Rings; 2.2 The Schur Index; 2.3 Locally Finite Skew Linear Groups of Positive Characteristic; 2.4 The Theorems of Zalesskii and Hartley & Shahabi; 2.5 Locally Finite Skew Linear Groups of Characteristic Zero; 3. LOCALLY FINITE-DIMENSIONAL DIVISION ALGEBRAS; 3.1 General Techniques; 3.2 Locally Nilpotent Groups; 3.3 Locally Soluble Groups; 3.4 The Upper Central Series | |
| 505 | 8 | |a 3.5 Engel Elements and Generalized Nilpotent Groups4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS; 4.1 Generalities and Examples; 4.2 Residual Finiteness; 4.3 Residual Nilpotence; 4.4 Division Rings of Quotients of Group Algebras; 4.5 Free Subgroups of Normal Subgroups of General Linear Groups; 4.6 Universal Enveloping Algebras of Lie Algebras; 5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS; 5.1 Normal Subgroups of Linear Groups; 5.2 Automorphisms of Certain Semisimple Algebras; 5.3 Recognizing Crossed Products; 5.4 Locally Finite Normal Subgroups of Skew Linear Groups | |
| 505 | 8 | |a 5.5 Locally Finite-Dimensional Division Algebras5.6 Soluble Normal Subgroups of Skew Linear Groups; 5.7 Generalized Soluble Groups; 6 AN APPLICATION TO GROUP RINGS; 6.1 Preliminaries; 6.2 Soluble Groups; 6.3 Locally Finite Groups; BIBLIOGRAPHY; NOTATION INDEX; AUTHOR INDEX; GENERAL INDEX | |
| 546 | |a English. | ||
| 650 | 0 | |a Finite groups. |0 http://id.loc.gov/authorities/subjects/sh85048354 | |
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| 650 | 0 | |a Skew fields. |0 http://id.loc.gov/authorities/subjects/sh85123128 | |
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| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
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| author2 | Wehrfritz, Bertram A. F. |
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| callnumber-raw | QA171 .S588 1986eb |
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| contents | Cover; Title; Copyright; Contents; 1. BASIC CONCEPTS; 1.1 Irreducibility; 1.2 Absolute Irreducibility; 1.3 Unipotence; 1.4 Constructions; 2. FINITE AND LOCALLY FINITE GROUPS; 2.1 Finite Subgroups of Division Rings; 2.2 The Schur Index; 2.3 Locally Finite Skew Linear Groups of Positive Characteristic; 2.4 The Theorems of Zalesskii and Hartley & Shahabi; 2.5 Locally Finite Skew Linear Groups of Characteristic Zero; 3. LOCALLY FINITE-DIMENSIONAL DIVISION ALGEBRAS; 3.1 General Techniques; 3.2 Locally Nilpotent Groups; 3.3 Locally Soluble Groups; 3.4 The Upper Central Series 3.5 Engel Elements and Generalized Nilpotent Groups4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS; 4.1 Generalities and Examples; 4.2 Residual Finiteness; 4.3 Residual Nilpotence; 4.4 Division Rings of Quotients of Group Algebras; 4.5 Free Subgroups of Normal Subgroups of General Linear Groups; 4.6 Universal Enveloping Algebras of Lie Algebras; 5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS; 5.1 Normal Subgroups of Linear Groups; 5.2 Automorphisms of Certain Semisimple Algebras; 5.3 Recognizing Crossed Products; 5.4 Locally Finite Normal Subgroups of Skew Linear Groups 5.5 Locally Finite-Dimensional Division Algebras5.6 Soluble Normal Subgroups of Skew Linear Groups; 5.7 Generalized Soluble Groups; 6 AN APPLICATION TO GROUP RINGS; 6.1 Preliminaries; 6.2 Soluble Groups; 6.3 Locally Finite Groups; BIBLIOGRAPHY; NOTATION INDEX; AUTHOR INDEX; GENERAL INDEX |
| ctrlnum | (OCoLC)839547826 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn839547826 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:18Z |
| institution | BVB |
| isbn | 9781107361379 1107361370 9780511600630 0511600631 1139881779 9781139881777 1107366283 9781107366282 1107371007 9781107371002 1107368626 9781107368620 1299404073 9781299404076 1107363829 9781107363823 |
| issn | 0076-0052 ; |
| language | English |
| oclc_num | 839547826 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (253 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Cambridge University Press, |
| record_format | marc |
| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series, |
| spelling | Shirvani, M. http://id.loc.gov/authorities/names/n85373094 Skew linear groups / M. Shirvani and B.A.F. Wehrfritz. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, ©1986. 1 online resource (253 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series, 0076-0052 ; 118 Includes bibliographical references (pages 227-236) and indexes. Includes indexes. Print version record. This book is concerned with subgroups of groups of the form GL(n, D) for some division ring D. In it the authors bring together many of the advances in the theory of skew linear groups. Some aspects of skew linear groups are similar to those for linear groups, however there are often significant differences either in the method of proof or the results themselves. Topics covered in this volume include irreducibility, unipotence, locally finite-dimensional division algebras, and division algebras associated with polycyclic groups. Both authors are experts in this area of current interest in group theory, and algebraists and research students will find this an accessible account of the subject. Cover; Title; Copyright; Contents; 1. BASIC CONCEPTS; 1.1 Irreducibility; 1.2 Absolute Irreducibility; 1.3 Unipotence; 1.4 Constructions; 2. FINITE AND LOCALLY FINITE GROUPS; 2.1 Finite Subgroups of Division Rings; 2.2 The Schur Index; 2.3 Locally Finite Skew Linear Groups of Positive Characteristic; 2.4 The Theorems of Zalesskii and Hartley & Shahabi; 2.5 Locally Finite Skew Linear Groups of Characteristic Zero; 3. LOCALLY FINITE-DIMENSIONAL DIVISION ALGEBRAS; 3.1 General Techniques; 3.2 Locally Nilpotent Groups; 3.3 Locally Soluble Groups; 3.4 The Upper Central Series 3.5 Engel Elements and Generalized Nilpotent Groups4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS; 4.1 Generalities and Examples; 4.2 Residual Finiteness; 4.3 Residual Nilpotence; 4.4 Division Rings of Quotients of Group Algebras; 4.5 Free Subgroups of Normal Subgroups of General Linear Groups; 4.6 Universal Enveloping Algebras of Lie Algebras; 5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS; 5.1 Normal Subgroups of Linear Groups; 5.2 Automorphisms of Certain Semisimple Algebras; 5.3 Recognizing Crossed Products; 5.4 Locally Finite Normal Subgroups of Skew Linear Groups 5.5 Locally Finite-Dimensional Division Algebras5.6 Soluble Normal Subgroups of Skew Linear Groups; 5.7 Generalized Soluble Groups; 6 AN APPLICATION TO GROUP RINGS; 6.1 Preliminaries; 6.2 Soluble Groups; 6.3 Locally Finite Groups; BIBLIOGRAPHY; NOTATION INDEX; AUTHOR INDEX; GENERAL INDEX English. Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Division rings. http://id.loc.gov/authorities/subjects/sh85038614 Matrix groups. http://id.loc.gov/authorities/subjects/sh85082222 Skew fields. http://id.loc.gov/authorities/subjects/sh85123128 Groupes finis. Corps gauches. Groupes de matrices. MATHEMATICS Group Theory. bisacsh Skew fields fast Division rings fast Finite groups fast Matrix groups fast Schiefgruppenring gnd http://d-nb.info/gnd/4179550-7 Endliche Gruppe gnd Groupes finis. ram Corps gauches. ram Matrices, Groupes de. ram Wehrfritz, Bertram A. F. http://id.loc.gov/authorities/names/n85373095 Print version: Shirvani, M. Skew linear groups. Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1986 0521339251 (DLC) 86026405 (OCoLC)14376796 London Mathematical Society lecture note series ; 118. 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=552392 Volltext |
| spellingShingle | Shirvani, M. Skew linear groups / London Mathematical Society lecture note series ; Cover; Title; Copyright; Contents; 1. BASIC CONCEPTS; 1.1 Irreducibility; 1.2 Absolute Irreducibility; 1.3 Unipotence; 1.4 Constructions; 2. FINITE AND LOCALLY FINITE GROUPS; 2.1 Finite Subgroups of Division Rings; 2.2 The Schur Index; 2.3 Locally Finite Skew Linear Groups of Positive Characteristic; 2.4 The Theorems of Zalesskii and Hartley & Shahabi; 2.5 Locally Finite Skew Linear Groups of Characteristic Zero; 3. LOCALLY FINITE-DIMENSIONAL DIVISION ALGEBRAS; 3.1 General Techniques; 3.2 Locally Nilpotent Groups; 3.3 Locally Soluble Groups; 3.4 The Upper Central Series 3.5 Engel Elements and Generalized Nilpotent Groups4. DIVISION RINGS ASSOCIATED WITH POLYCYCLIC GROUPS; 4.1 Generalities and Examples; 4.2 Residual Finiteness; 4.3 Residual Nilpotence; 4.4 Division Rings of Quotients of Group Algebras; 4.5 Free Subgroups of Normal Subgroups of General Linear Groups; 4.6 Universal Enveloping Algebras of Lie Algebras; 5. NORMAL SUBGROUPS OF ABSOLUTELY IRREDUCIBLE GROUPS; 5.1 Normal Subgroups of Linear Groups; 5.2 Automorphisms of Certain Semisimple Algebras; 5.3 Recognizing Crossed Products; 5.4 Locally Finite Normal Subgroups of Skew Linear Groups 5.5 Locally Finite-Dimensional Division Algebras5.6 Soluble Normal Subgroups of Skew Linear Groups; 5.7 Generalized Soluble Groups; 6 AN APPLICATION TO GROUP RINGS; 6.1 Preliminaries; 6.2 Soluble Groups; 6.3 Locally Finite Groups; BIBLIOGRAPHY; NOTATION INDEX; AUTHOR INDEX; GENERAL INDEX Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Division rings. http://id.loc.gov/authorities/subjects/sh85038614 Matrix groups. http://id.loc.gov/authorities/subjects/sh85082222 Skew fields. http://id.loc.gov/authorities/subjects/sh85123128 Groupes finis. Corps gauches. Groupes de matrices. MATHEMATICS Group Theory. bisacsh Skew fields fast Division rings fast Finite groups fast Matrix groups fast Schiefgruppenring gnd http://d-nb.info/gnd/4179550-7 Endliche Gruppe gnd Groupes finis. ram Corps gauches. ram Matrices, Groupes de. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048354 http://id.loc.gov/authorities/subjects/sh85038614 http://id.loc.gov/authorities/subjects/sh85082222 http://id.loc.gov/authorities/subjects/sh85123128 http://d-nb.info/gnd/4179550-7 |
| title | Skew linear groups / |
| title_auth | Skew linear groups / |
| title_exact_search | Skew linear groups / |
| title_full | Skew linear groups / M. Shirvani and B.A.F. Wehrfritz. |
| title_fullStr | Skew linear groups / M. Shirvani and B.A.F. Wehrfritz. |
| title_full_unstemmed | Skew linear groups / M. Shirvani and B.A.F. Wehrfritz. |
| title_short | Skew linear groups / |
| title_sort | skew linear groups |
| topic | Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Division rings. http://id.loc.gov/authorities/subjects/sh85038614 Matrix groups. http://id.loc.gov/authorities/subjects/sh85082222 Skew fields. http://id.loc.gov/authorities/subjects/sh85123128 Groupes finis. Corps gauches. Groupes de matrices. MATHEMATICS Group Theory. bisacsh Skew fields fast Division rings fast Finite groups fast Matrix groups fast Schiefgruppenring gnd http://d-nb.info/gnd/4179550-7 Endliche Gruppe gnd Groupes finis. ram Corps gauches. ram Matrices, Groupes de. ram |
| topic_facet | Finite groups. Division rings. Matrix groups. Skew fields. Groupes finis. Corps gauches. Groupes de matrices. MATHEMATICS Group Theory. Skew fields Division rings Finite groups Matrix groups Schiefgruppenring Endliche Gruppe Matrices, Groupes de. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=552392 |
| work_keys_str_mv | AT shirvanim skewlineargroups AT wehrfritzbertramaf skewlineargroups |