The structure of groups of prime power order:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Oxford Univ. Press
2002
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society monographs
New series ; 27 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 334 S. |
| ISBN: | 0198535481 |
Staff View
MARC
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| 245 | 1 | 0 | |a The structure of groups of prime power order |c C. R. Leedham-Green and S. McKay |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Oxford |b Oxford Univ. Press |c 2002 | |
| 300 | |a XII, 334 S. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Preliminaries
1.1 Commutators 1
1.2 Basic theory of finite p groups 13
1.3 Local fields 18
2 New groups from old
2.1 Group actions and extensions 25
2.2 Pull backs and central products 30
2.3 Wreath products, imprimitivity and actions on trees 38
2.4 Iterated wreath products of Cp 47
3 p groups of maximal class
3.1 Definition and examples of p groups of maximal class 52
3.2 The degree of commutativity of p groups of maximal class 56
3.3 The power structure of p groups of maximal class 59
3.4 Bounding the degree of commutativity 63
4 Finite p groups acting uniserially
4.1 Uniserial actions on finite p groups 70
4.2 Wreath products and uniserial action 76
4.3 Uniserial action on finite abelian p groups 85
4.4 The Sylow p subgroups of GL(rf, Z/pnZ) 88
4.5 The maximal p subgroups of GL(d, Z) 91
5 Using Lie algebra theory to find bounds
5.1 Preliminaries on Lie algebras 96
5.2 Jacobson s version of Engel s theorem 98
5.3 Application to p groups of maximal class 101
Contents xi
5.4 Settled p groups 102
5.5 Automorphisms with p fixed points 108
6 The proof of Conjecture A using powerful p groups
6.1 Powerful p groups 113
6.2 Strongly hereditarily powerful subgroups 119
6.3 Application to p groups of small coclass 123
6.4 Conjecture A 128
7 Pro p groups
7.1 Topological groups 132
7.2 Pro finite groups 136
7.3 Free groups 142
7.4 Pro p groups of finite coclass 145
8 Constructing finite p groups
8.1 Realizations and twistings 152
8.2 Constructing p groups of maximal class 154
8.3 Twisting homomorphisms for p groups of maximal class 159
8.4 Constructible p groups 165
9 Homological algebra
9.1 Derived functors 172
9.2 Double complexes and spectral sequences 182
9.3 Ext and Tor 192
9.4 The homology and cohomology of groups 196
9.5 Interpretations of group homology and cohomology 208
10 Uniserial p adic space groups
10.1 Primitive p adic representations 219
10.2 The maximal irreducible p subgroups of GL(d, Qp) 231
10.3 Lattices for uniserial p adic space groups 234
10.4 Embedding in a split space group 239
10.5 Bounding the coclass of uniserial 2 adic space groups 241
xii Contents
11 The structure of finite p groups
11.1 Properties of settled p groups 251
11.2 Preliminary structure theorems and generic bounds 254
11.3 Structure theorems for p groups of coclass r 258
11.4 Calculating the twisting homomorphisms 265
12 Beyond coclass
12.1 Finiteness conditions on pro p groups 269
12.2 p groups of rank 3, width 2 and obliquity 0 272
12.3 The Grigorchuk group 281
12.4 The Nottingham group 298
Bibliography 318
Symbol index 322
Index 330
|
| any_adam_object | 1 |
| author | Leedham-Green, Charles Richard 1940- McKay, Susan |
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| id | DE-604.BV014208614 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:59:37Z |
| institution | BVB |
| isbn | 0198535481 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009740990 |
| oclc_num | 59407394 |
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| owner_facet | DE-355 DE-BY-UBR DE-29T DE-20 DE-703 DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-11 |
| physical | XII, 334 S. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | London Mathematical Society monographs |
| series2 | London Mathematical Society monographs : New series |
| spelling | Leedham-Green, Charles Richard 1940- Verfasser (DE-588)115706046 aut The structure of groups of prime power order C. R. Leedham-Green and S. McKay 1. publ. Oxford Oxford Univ. Press 2002 XII, 334 S. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society monographs : New series 27 Automorphismes Groupes finis Automorphisms Finite groups p-Gruppe (DE-588)4174108-0 gnd rswk-swf p-Gruppe (DE-588)4174108-0 s DE-604 McKay, Susan Verfasser aut London Mathematical Society monographs New series ; 27 (DE-604)BV045355493 27 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009740990&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Leedham-Green, Charles Richard 1940- McKay, Susan The structure of groups of prime power order London Mathematical Society monographs Automorphismes Groupes finis Automorphisms Finite groups p-Gruppe (DE-588)4174108-0 gnd |
| subject_GND | (DE-588)4174108-0 |
| title | The structure of groups of prime power order |
| title_auth | The structure of groups of prime power order |
| title_exact_search | The structure of groups of prime power order |
| title_full | The structure of groups of prime power order C. R. Leedham-Green and S. McKay |
| title_fullStr | The structure of groups of prime power order C. R. Leedham-Green and S. McKay |
| title_full_unstemmed | The structure of groups of prime power order C. R. Leedham-Green and S. McKay |
| title_short | The structure of groups of prime power order |
| title_sort | the structure of groups of prime power order |
| topic | Automorphismes Groupes finis Automorphisms Finite groups p-Gruppe (DE-588)4174108-0 gnd |
| topic_facet | Automorphismes Groupes finis Automorphisms Finite groups p-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009740990&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045355493 |
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