Subgroups of finite groups:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Groningen
Wolters-Noordhoff
1969
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 142 S. |
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MARC
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Record in the Search Index
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| adam_text | CONTENTS
Translator s Preface 5
Preface 7
Notation Index 9
Contents 13
Chapter 1
Sylow /7 properties of Finite Groups 17
1.1 The i7 method for the investigation of groups 17
1.2 (5 properties and universal properties of finite groups . ... 18
1.3 Sylow /7 properties of finite groups 18
1.4 Necessary and sufficient conditions for properties Csn and Esn 19
1.5 Theorems of Schur and Schur Zassenhaus 26
1.6 A necessary and sufficient condition for property Cn . . . . 32
1.7 The property CsnjI, 34
1.8 /7 solvable groups 35
1.9 Maximal subgroups of /7 solvable groups 37
1.10 Non nilpotent subgroups of finite groups 43
1.11 The monomial homomorphism 44
1.12 p decomposable subgroups 48
1.13 A decomposition of /7 solvable groups into direct products
of subgroups 51
1.14 77 supersolvable groups 54
1.15 /7 separable groups 57
1.16 Necessary conditions for the existence of subgroups . ... 58
14 Contents
Chapter 2
Factorizations of Finite Groups Based on the Indices of Chief and
Composition Series 61
2.1 The direct and inverse problems of factorization for finite
groups 61
2.2 A factorization lemma . 62
2.3 A factorization for finite groups, using a chief series .... 62
2.4 Composition block factorizations of finite groups 76
2.5 77 factorizations of finite groups 77
Chapter 3
A Method for Finding Subgroups by Means of Indexials 79
3.1 The method of indexials 79
3.2 Arithmetic indexials of finite groups 79
3.3 The definition of a constructive indexial 80
3.4 The measure of solvability for finite groups 81
3.5 Extensions of indexials 81
3.6 Isomorphism lemmas 84
3.7 The fundamental theorem on the existence of regular Sylow
extensions of indexials 85
3.8 Directed indexials 100
3.9 Applications of the method of indexials 101
3.10 c separable groups 106
3.11 A further example of a regular indexial 108
Chapter 4
Complexes of Non Nilpotent Subgroups , . • 109
4.1 Introduction 109
4.2 Additional notation 110
4.3 Subgroups of type Sp and /75 complexes of subgroups. . . .111
Contents 15
4.4 nSC complexes of subgroups 115
4.5 /7SC complexes of subgroups and dispersibility of groups. . 120
4.6 /7S complexes of subgroups and dispersibility of groups . . 123
4.7 Non decomposable/7 complexes of subgroups 126
Bibliography 133
Index 141
|
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| author_facet | Čunichin, Sergej A. |
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| author_sort | Čunichin, Sergej A. |
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| building | Verbundindex |
| bvnumber | BV002745241 |
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| discipline | Mathematik |
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| id | DE-604.BV002745241 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:49:00Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001755281 |
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| physical | 142 S. |
| psigel | HUB-ZB011200801 |
| publishDate | 1969 |
| publishDateSearch | 1969 |
| publishDateSort | 1969 |
| publisher | Wolters-Noordhoff |
| record_format | marc |
| spelling | Čunichin, Sergej A. Verfasser aut Podgruppy konečnych grupp Subgroups of finite groups S. A. Chunikhin Groningen Wolters-Noordhoff 1969 142 S. txt rdacontent n rdamedia nc rdacarrier Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Untergruppe (DE-588)4224972-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Untergruppe (DE-588)4224972-7 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Čunichin, Sergej A. Subgroups of finite groups Endliche Gruppe (DE-588)4014651-0 gnd Untergruppe (DE-588)4224972-7 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4224972-7 |
| title | Subgroups of finite groups |
| title_alt | Podgruppy konečnych grupp |
| title_auth | Subgroups of finite groups |
| title_exact_search | Subgroups of finite groups |
| title_full | Subgroups of finite groups S. A. Chunikhin |
| title_fullStr | Subgroups of finite groups S. A. Chunikhin |
| title_full_unstemmed | Subgroups of finite groups S. A. Chunikhin |
| title_short | Subgroups of finite groups |
| title_sort | subgroups of finite groups |
| topic | Endliche Gruppe (DE-588)4014651-0 gnd Untergruppe (DE-588)4224972-7 gnd |
| topic_facet | Endliche Gruppe Untergruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001755281&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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