Subnormal subgroups of groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Pr.
1987
|
| Schriftenreihe: | Oxford mathematical monographs
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 253 S. |
| ISBN: | 019853552X |
Internformat
MARC
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| 245 | 1 | 0 | |a Subnormal subgroups of groups |c John C. Lennox ; Stewart E. Stonehewer |
| 264 | 1 | |a Oxford |b Clarendon Pr. |c 1987 | |
| 300 | |a XIII, 253 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804115118055751680 |
|---|---|
| adam_text | CONTENTS
INDEX OF NOTATION xi
1 THE JOIN OF TWO SUBNORMAL SUBGROUPS 1
1.1 Definitions and first properties 1
1.2 First results on joins 3
1.3 Wielandt s Join Theorem 6
1.4 The class S of groups with the subnormal join property 10
1.5 Counterexamples 14
1.6 Subnormal coalescence and the permutizer 21
1.7 Some subnormal coalition classes 32
2 THE JOIN OF MANY SUBNORMAL SUBGROUPS 42
2.1 Internal structure of joins of finitely many subnormal subgroups 42
2.2 Internal structure of joins of arbitrarily many subnormal subgroups 50
2.3 Subnormal composition factors 55
2.4 Seriality of joins and the class S 66
2.5 Baer groups 74
2.6 The class S°° (continued) 84
2.7 The commutator of two subnormal subgroups 88
3 THE DERIVED AND LOWER CENTRAL SERIES OF A
JOIN OF SUBNORMAL SUBGROUPS 89
3.1 The derived series of a join of subnormal subgroups 89
3.2 Applications to the join problem and coalescence 97
3.3 The lower central series of a join of subnormal subgroups 100
3.4 Further applications to the join problem 116
3.5 More on the classes S and S°° 123
4 THE PERMUTABILITY OF SUBNORMAL SUBGROUPS 128
4.1 Wielandt s theory of operators 128
4.2 The permutability properties of operators 133
4.3 Roseblade s Permutability Theorem 138
4.4 Permutability properties of soluble and nilpotent residuals of
subnormal subgroups 142
4.5 Relative normalizing and centralizing properties 146
4.6 Universal normalizing properties: the Wielandt subgroup 151
5 THE JOIN PROBLEM—A CRITERION 155
5.1 Williams Join Theorem 155
5.2 Examples 159
5.3 Persistent properties of nilpotent groups 161
5.4 Proofs of the main theorems 165
6 GROUPS WITH MANY SUBNORMAL SUBGROUPS 171
6.1 Groups in which every subgroup is subnormal 171
6.2 Non nilpotent groups with every subgroup subnormal 180
6.3 Groups in which every subgroup is almost subnormal 191
x CONTENTS
6.4 Groups with all subnormal subgroups of bounded defect 197
6.5 Groups with the subnormal intersection property 209
7 CRITERIA FOR SUBNORMALITY 213
7.1 Permutability 213
7.2 Permutability of conjugates of subgroups 220
7.3 The Wielandt maximizer lemmas 222
7.4 Groups satisfying the maximal condition 229
7.5 Polycyclic by finite groups 232
7.6 Join subnormality 234
7.7 The subnormalizer of a subgroup 238
BIBLIOGRAPHY 243
GENERALIZATIONS OF RESULTS 250
INDEX 251
|
| any_adam_object | 1 |
| author | Lennox, John 1943- Stonehewer, Stewart E. |
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| discipline | Mathematik |
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| id | DE-604.BV000669701 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:17:31Z |
| institution | BVB |
| isbn | 019853552X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000417927 |
| oclc_num | 13426048 |
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| physical | XIII, 253 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Clarendon Pr. |
| record_format | marc |
| series2 | Oxford mathematical monographs |
| spelling | Lennox, John 1943- Verfasser (DE-588)123765021 aut Subnormal subgroups of groups John C. Lennox ; Stewart E. Stonehewer Oxford Clarendon Pr. 1987 XIII, 253 S. txt rdacontent n rdamedia nc rdacarrier Oxford mathematical monographs Group rings Group theory Nachinvariante Untergruppe (DE-588)4470783-6 gnd rswk-swf Nachinvariante Untergruppe (DE-588)4470783-6 s DE-604 Stonehewer, Stewart E. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lennox, John 1943- Stonehewer, Stewart E. Subnormal subgroups of groups Group rings Group theory Nachinvariante Untergruppe (DE-588)4470783-6 gnd |
| subject_GND | (DE-588)4470783-6 |
| title | Subnormal subgroups of groups |
| title_auth | Subnormal subgroups of groups |
| title_exact_search | Subnormal subgroups of groups |
| title_full | Subnormal subgroups of groups John C. Lennox ; Stewart E. Stonehewer |
| title_fullStr | Subnormal subgroups of groups John C. Lennox ; Stewart E. Stonehewer |
| title_full_unstemmed | Subnormal subgroups of groups John C. Lennox ; Stewart E. Stonehewer |
| title_short | Subnormal subgroups of groups |
| title_sort | subnormal subgroups of groups |
| topic | Group rings Group theory Nachinvariante Untergruppe (DE-588)4470783-6 gnd |
| topic_facet | Group rings Group theory Nachinvariante Untergruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000417927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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