Products of groups:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Pr.
1992
|
| Series: | Oxford mathematical monographs
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 220 S. |
| ISBN: | 0198535759 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Notation xi
1. ELEMENTARY PROPERTIES OF FACTORIZED
GROUPS 1
1.1 The factorizer 1
1.2 Normalizers, indices, and chain conditions 5
1.3 Sylow subgroups 8
1.4 Existence of factorizations 10
2. PRODUCTS OF NILPOTENT GROUPS 14
2.1 Products of abelian groups 14
2.2 Products of central by finite groups 18
2.3 Residually finite products of abelian by finite groups 23
2.4 The theorem of Kegel and Wielandt 26
2.5 The structure of a finite product of nilpotent groups 33
3. PRODUCTS OF PERIODIC GROUPS 42
3.1 An example of a non periodic product of two periodic
groups 42
3.2 Soluble products of periodic groups 46
3.3 Soluble products of groups of finite exponent 53
4. PRODUCTS OF GROUPS OF FINITE RANK 63
4.1 Rank formulae 63
4.2 The number of generators of a finite soluble group 69
4.3 Factorized groups with finite Priifer rank 75
4.4 Soluble products of polycyclic groups 80
4.5 Products of a nilpotent and a polycyclic group 82
4.6 Soluble products of groups of finite rank 91
5. SPLITTING AND CONJUGACY THEOREMS 104
5.1 Cohomology of groups 104
5.2 Cohomological machinery 111
x CONTENTS
5.3 Splitting and conjugacy 115
5.4 Near splitting and near conjugacy 128
6. TRIPLY FACTORIZED GROUPS 135
6.1 Examples of groups with an abelian triple factorization 135
6.2 Lower central factors and tensor products 142
6.3 Groups with a nilpotent triple factorization 144
6.4 FC nilpotent and FC hypercentral groups 154
6.5 Groups with a supersoluble triple factorization 158
6.6 Trifactorized groups 168
7. SOME FURTHER TOPICS 182
7.1 The inside outside problem 182
7.2 The Fitting length of a soluble product of nilpotent
groups 187
7.3 Products of an abelian and an FC group 192
7.4 Products of locally cyclic groups 198
7.5 Subnormal subgroups of factorized groups 201
7.6 Groups factorized by finitely many subgroups 205
BIBLIOGRAPHY 211
INDEX 219
|
| any_adam_object | 1 |
| author | Amberg, Bernhard 1940- Franciosi, Silvana De Giovanni, Francesco |
| author_GND | (DE-588)131436384 |
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| author_sort | Amberg, Bernhard 1940- |
| author_variant | b a ba s f sf g f d gf gfd |
| building | Verbundindex |
| bvnumber | BV007193191 |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)246896618 (DE-599)BVBBV007193191 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV007193191 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:57:23Z |
| institution | BVB |
| isbn | 0198535759 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004601218 |
| oclc_num | 246896618 |
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| physical | XII, 220 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Clarendon Pr. |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Amberg, Bernhard 1940- Verfasser (DE-588)131436384 aut Products of groups Bernhard Amberg, Silvana Franciosi and Francesco de Giovanni Oxford Clarendon Pr. 1992 XII, 220 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Produkt Mathematik (DE-588)4126359-5 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 s Faktorisierung (DE-588)4128927-4 s DE-604 Gruppentheorie (DE-588)4072157-7 s Produkt Mathematik (DE-588)4126359-5 s DE-188 Franciosi, Silvana Verfasser aut De Giovanni, Francesco Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Amberg, Bernhard 1940- Franciosi, Silvana De Giovanni, Francesco Products of groups Gruppentheorie (DE-588)4072157-7 gnd Produkt Mathematik (DE-588)4126359-5 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Faktorisierung (DE-588)4128927-4 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4126359-5 (DE-588)4022379-6 (DE-588)4128927-4 |
| title | Products of groups |
| title_auth | Products of groups |
| title_exact_search | Products of groups |
| title_full | Products of groups Bernhard Amberg, Silvana Franciosi and Francesco de Giovanni |
| title_fullStr | Products of groups Bernhard Amberg, Silvana Franciosi and Francesco de Giovanni |
| title_full_unstemmed | Products of groups Bernhard Amberg, Silvana Franciosi and Francesco de Giovanni |
| title_short | Products of groups |
| title_sort | products of groups |
| topic | Gruppentheorie (DE-588)4072157-7 gnd Produkt Mathematik (DE-588)4126359-5 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Faktorisierung (DE-588)4128927-4 gnd |
| topic_facet | Gruppentheorie Produkt Mathematik Gruppe Mathematik Faktorisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004601218&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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