Groups of prime power order.: Volume 4 /
This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa's theorem on p-groups with tw...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston :
De Gruyter,
©2016.
|
| Schriftenreihe: | De Gruyter expositions in mathematics ;
61. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa's theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra. |
| Beschreibung: | 165 p-groups G all of whose subgroups containing ∅G) as a subgroup of index p are minimal nonabelian |
| Beschreibung: | 1 online resource (476 pages) |
| Bibliographie: | Includes bibliographical references and indexes. |
| ISBN: | 9783110281477 3110281473 9783110281484 3110281481 9783110381559 3110381559 |
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| 245 | 1 | 0 | |a Groups of prime power order. |n Volume 4 / |c Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and 4 others]. |
| 260 | |a Berlin ; |a Boston : |b De Gruyter, |c ©2016. | ||
| 300 | |a 1 online resource (476 pages) | ||
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| 504 | |a Includes bibliographical references and indexes. | ||
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| 500 | |a 165 p-groups G all of whose subgroups containing ∅G) as a subgroup of index p are minimal nonabelian | ||
| 505 | 0 | |a Content ; List of definitions and notations ; Preface ; 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p; 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups ; 147 p-groups with exactly two sizes of conjugate classes | |
| 505 | 8 | |a 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic 149 p-groups with many minimal nonabelian subgroups ; 150 The exponents of finite p-groups and their automorphism groups | |
| 505 | 8 | |a 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center 152 p-central p-groups ; 153 Some generalizations of 2-central 2-groups ; 154 Metacyclic p-groups covered by minimal nonabelian subgroups ; 155 A new type of Thompson subgroup | |
| 505 | 8 | |a 156 Minimal number of generators of a p-group, p> 2 157 Some further properties of p-central p-groups ; 158 On extraspecial normal subgroups of p-groups ; 159 2-groups all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup; 160 p-groups, p> 2, all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup | |
| 505 | 8 | |a 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal 162 The centralizer equality subgroup in a p-group ; 163 Macdonald's theorem on p-groups all of whose proper subgroups are of class at most 2 ; 164 Partitions and Hp-subgroups of a p-group | |
| 520 | |a This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa's theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra. | ||
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| adam_text | |
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| author | Berkovich, I︠A︡. G., 1938- |
| author2 | Janko, Zvonimir, 1932- |
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| author_facet | Berkovich, I︠A︡. G., 1938- Janko, Zvonimir, 1932- |
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| author_sort | Berkovich, I︠A︡. G., 1938- |
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| contents | Content ; List of definitions and notations ; Preface ; 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p; 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups ; 147 p-groups with exactly two sizes of conjugate classes 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic 149 p-groups with many minimal nonabelian subgroups ; 150 The exponents of finite p-groups and their automorphism groups 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center 152 p-central p-groups ; 153 Some generalizations of 2-central 2-groups ; 154 Metacyclic p-groups covered by minimal nonabelian subgroups ; 155 A new type of Thompson subgroup 156 Minimal number of generators of a p-group, p> 2 157 Some further properties of p-central p-groups ; 158 On extraspecial normal subgroups of p-groups ; 159 2-groups all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup; 160 p-groups, p> 2, all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal 162 The centralizer equality subgroup in a p-group ; 163 Macdonald's theorem on p-groups all of whose proper subgroups are of class at most 2 ; 164 Partitions and Hp-subgroups of a p-group |
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| dewey-ones | 512 - Algebra |
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| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn945718242 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:27:07Z |
| institution | BVB |
| isbn | 9783110281477 3110281473 9783110281484 3110281481 9783110381559 3110381559 |
| language | English |
| oclc_num | 945718242 |
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| publishDateSearch | 2016 |
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| series | De Gruyter expositions in mathematics ; |
| series2 | De Gruyter Expositions in Mathematics ; |
| spelling | Berkovich, I︠A︡. G., 1938- http://id.loc.gov/authorities/names/n97085489 Groups of prime power order. Volume 4 / Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and 4 others]. Berlin ; Boston : De Gruyter, ©2016. 1 online resource (476 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier De Gruyter Expositions in Mathematics ; volume 61 Includes bibliographical references and indexes. Online resource; title from digital title page (viewed on March 30, 2016). 165 p-groups G all of whose subgroups containing ∅G) as a subgroup of index p are minimal nonabelian Content ; List of definitions and notations ; Preface ; 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p; 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups ; 147 p-groups with exactly two sizes of conjugate classes 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic 149 p-groups with many minimal nonabelian subgroups ; 150 The exponents of finite p-groups and their automorphism groups 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center 152 p-central p-groups ; 153 Some generalizations of 2-central 2-groups ; 154 Metacyclic p-groups covered by minimal nonabelian subgroups ; 155 A new type of Thompson subgroup 156 Minimal number of generators of a p-group, p> 2 157 Some further properties of p-central p-groups ; 158 On extraspecial normal subgroups of p-groups ; 159 2-groups all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup; 160 p-groups, p> 2, all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal 162 The centralizer equality subgroup in a p-group ; 163 Macdonald's theorem on p-groups all of whose proper subgroups are of class at most 2 ; 164 Partitions and Hp-subgroups of a p-group This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa's theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra. Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Algebra Intermediate. bisacsh Finite groups fast Group theory fast Group Theory. Order. Primes. Janko, Zvonimir, 1932- http://id.loc.gov/authorities/names/n2011014887 Print version: Berkovich, Yakov G. Groups of Prime Power Order 4 : Volume 4. Berlin/Boston : De Gruyter, ©2015 9783110281453 De Gruyter expositions in mathematics ; 61. http://id.loc.gov/authorities/names/n90653843 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1131257 Volltext |
| spellingShingle | Berkovich, I︠A︡. G., 1938- Groups of prime power order. De Gruyter expositions in mathematics ; Content ; List of definitions and notations ; Preface ; 145 p-groups all of whose maximal subgroups, except one, have derived subgroup of order ≤ p; 146 p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups ; 147 p-groups with exactly two sizes of conjugate classes 148 Maximal abelian and minimal nonabelian subgroups of some finite two-generator p-groups especially metacyclic 149 p-groups with many minimal nonabelian subgroups ; 150 The exponents of finite p-groups and their automorphism groups 151 p-groups all of whose nonabelian maximal subgroups have the largest possible center 152 p-central p-groups ; 153 Some generalizations of 2-central 2-groups ; 154 Metacyclic p-groups covered by minimal nonabelian subgroups ; 155 A new type of Thompson subgroup 156 Minimal number of generators of a p-group, p> 2 157 Some further properties of p-central p-groups ; 158 On extraspecial normal subgroups of p-groups ; 159 2-groups all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup; 160 p-groups, p> 2, all of whose cyclic subgroups A, B with A Â"B `"{1} generate an abelian subgroup 161 p-groups where all subgroups not contained in the Frattini subgroup are quasinormal 162 The centralizer equality subgroup in a p-group ; 163 Macdonald's theorem on p-groups all of whose proper subgroups are of class at most 2 ; 164 Partitions and Hp-subgroups of a p-group Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Algebra Intermediate. bisacsh Finite groups fast Group theory fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048354 http://id.loc.gov/authorities/subjects/sh85057512 |
| title | Groups of prime power order. |
| title_auth | Groups of prime power order. |
| title_exact_search | Groups of prime power order. |
| title_full | Groups of prime power order. Volume 4 / Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and 4 others]. |
| title_fullStr | Groups of prime power order. Volume 4 / Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and 4 others]. |
| title_full_unstemmed | Groups of prime power order. Volume 4 / Yakov Berkovich and Zvonimir Janko ; edited by Victor P. Maslov [and 4 others]. |
| title_short | Groups of prime power order. |
| title_sort | groups of prime power order |
| topic | Finite groups. http://id.loc.gov/authorities/subjects/sh85048354 Group theory. http://id.loc.gov/authorities/subjects/sh85057512 Groupes finis. Théorie des groupes. MATHEMATICS Algebra Intermediate. bisacsh Finite groups fast Group theory fast |
| topic_facet | Finite groups. Group theory. Groupes finis. Théorie des groupes. MATHEMATICS Algebra Intermediate. Finite groups Group theory |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1131257 |
| work_keys_str_mv | AT berkovichiag groupsofprimepowerordervolume4 AT jankozvonimir groupsofprimepowerordervolume4 |