Presentations of groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1997
|
| Edition: | 2. ed. |
| Series: | London Mathematical Society: London Mathematical Society student texts
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 216 S. graph. Darst. |
| ISBN: | 0521585422 |
Staff View
MARC
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| 650 | 7 | |a ÁLGEBRA HOMOLÓGICA |2 larpcal | |
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Record in the Search Index
| _version_ | 1804126086224674817 |
|---|---|
| adam_text | CONTENTS
Preface xi
1. Free Groups 1
1.1 Definition and elementary properties 1
1.2 Existence of F(X) 4
1.3 Further properties of F(X) 7
Exercises 11
2. Schreier s Method 14
2.1 The well ordering of F 14
2.2 The Schreier transversal 16
2.3 The Schreier generators 18
2.4 Decomposition of the set A 19
2.5 Freeness of the generators B 20
2.6 Conclusion 22
Exercises 24
3. Nielsen s Method 26
3.1 The finitely generated case 26
3.2 Example 1 32
3.3 The general case 33
3.4 Further applications 34
Exercise 39
4. Free Presentations of Groups 41
4.1 Basic concepts 41
4.2 Induced homomorphisms 42
4.3 Direct products 44
4.4 Tietze transformations 45
4.5 van Kampen diagrams 51
Exercises 55
5. Some Popular Groups 58
5.1 The quaternions 58
viii Contents
5.2 The Heisenberg group 60
5.3 Symmetric groups 61
5.4 Semi direct products 64
5.5 Groups of symmetries 66
5.6 Polynomials under substitution 68
5.7 The rational numbers 69
Exercises 72
6. Finitely generated Abelian Groups 74
6.1 Groups made abelian 74
6.2 Free abelian groups 75
6.3 Change of generators 78
6.4 The invariant factor theorem for matrices 80
6.5 The basis theorem 83
Exercises 85
7. Finite Groups with few Relations 87
7.1 Metacyclic groups 88
7.2 Interesting groups with three generators 92
7.3 Cyclically presented groups 95
Exercises 97
8. Coset Enumeration 100
8.1 The basic method 100
8.2 A refinement 108
Exercises 114
9. Presentations of Subgroups 116
9.1 The method 116
9.2 Alternating groups 118
9.3 Braid groups 119
9.4 von Dyck groups 121
9.5 Triangle groups 127
9.6 Free products 128
9.7 HNN extensions 129
9.8 TheSchurmultiplicator 132
Exercises 133
Contents ix
10. Presentations of Group Extensions 136
10.1 Basic concepts 136
10.2 The main theorem 138
10.3 Special cases 141
10.4 Finite p groups 143
Exercises 144
11. Relation Modules 146
11.1 G modules 146
11.2 The augmentation ideal 149
11.3 Derivations 151
11.4 Free differential calculus 153
11.5 The fundamental isomorphsim 155
Exercises 159
12. An Algorithm for N/AT 160
12.1 TheJacobian 161
12.2 The proof 161
12.3 Example 162
Exercises 167
13. Finite p groups 168
13.1 Review of elementary properties 168
13.2 Power commutator presentations 170
13.3 modp modules 173
Exercises 177
14. The Nilpotent Quotient Algorithm 178
14.1 The algorithm 178
14.2 An example 180
14.3 An improvement 184
Exercises 185
15. The Golod Shafarevich Theorem 186
15.1 The proof 186
15.2 An example 188
x Contents
15.3 Related results 189
Exercises 190
16. Proving some Groups Infinite 191
16.1 Dimension subgroups 191
16.2 The Gaschiitz Newman formulae 193
¦ 16.3 Newman s criterion 196
16.4 Fibonacci update 199
Exercises 200
Guide to the literature and references 201
Index 211
Dramatis personae 216
|
| any_adam_object | 1 |
| author | Johnson, David L. 1943- |
| author_GND | (DE-588)115496629 |
| author_facet | Johnson, David L. 1943- |
| author_role | aut |
| author_sort | Johnson, David L. 1943- |
| author_variant | d l j dl dlj |
| building | Verbundindex |
| bvnumber | BV011560368 |
| callnumber-first | Q - Science |
| callnumber-label | QA174 |
| callnumber-raw | QA174 |
| callnumber-search | QA174 |
| callnumber-sort | QA 3174 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| ctrlnum | (OCoLC)35688069 (DE-599)BVBBV011560368 |
| dewey-full | 512/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:11:51Z |
| institution | BVB |
| isbn | 0521585422 |
| language | English |
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| owner_facet | DE-703 |
| physical | X, 216 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | London Mathematical Society: London Mathematical Society student texts |
| series2 | London Mathematical Society: London Mathematical Society student texts |
| spelling | Johnson, David L. 1943- Verfasser (DE-588)115496629 aut Presentations of groups D. L. Johnson 2. ed. Cambridge [u.a.] Cambridge Univ. Press 1997 X, 216 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society: London Mathematical Society student texts 15 COHOMOLOGIA DE GRUPOS larpcal TEORIA DOS GRUPOS larpcal ÁLGEBRA HOMOLÓGICA larpcal ÁLGEBRA larpcal Presentations of groups (Mathematics) Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd rswk-swf Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Kombinatorische Gruppentheorie (DE-588)4219556-1 s DE-604 Gruppentheorie (DE-588)4072157-7 s Darstellungstheorie (DE-588)4148816-7 s 1\p DE-604 Gruppe Mathematik (DE-588)4022379-6 s 2\p DE-604 Darstellung Mathematik (DE-588)4128289-9 s 3\p DE-604 London Mathematical Society: London Mathematical Society student texts 15 (DE-604)BV000841726 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007784291&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Johnson, David L. 1943- Presentations of groups London Mathematical Society: London Mathematical Society student texts COHOMOLOGIA DE GRUPOS larpcal TEORIA DOS GRUPOS larpcal ÁLGEBRA HOMOLÓGICA larpcal ÁLGEBRA larpcal Presentations of groups (Mathematics) Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| subject_GND | (DE-588)4219556-1 (DE-588)4148816-7 (DE-588)4072157-7 (DE-588)4128289-9 (DE-588)4022379-6 |
| title | Presentations of groups |
| title_auth | Presentations of groups |
| title_exact_search | Presentations of groups |
| title_full | Presentations of groups D. L. Johnson |
| title_fullStr | Presentations of groups D. L. Johnson |
| title_full_unstemmed | Presentations of groups D. L. Johnson |
| title_short | Presentations of groups |
| title_sort | presentations of groups |
| topic | COHOMOLOGIA DE GRUPOS larpcal TEORIA DOS GRUPOS larpcal ÁLGEBRA HOMOLÓGICA larpcal ÁLGEBRA larpcal Presentations of groups (Mathematics) Kombinatorische Gruppentheorie (DE-588)4219556-1 gnd Darstellungstheorie (DE-588)4148816-7 gnd Gruppentheorie (DE-588)4072157-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Gruppe Mathematik (DE-588)4022379-6 gnd |
| topic_facet | COHOMOLOGIA DE GRUPOS TEORIA DOS GRUPOS ÁLGEBRA HOMOLÓGICA ÁLGEBRA Presentations of groups (Mathematics) Kombinatorische Gruppentheorie Darstellungstheorie Gruppentheorie Darstellung Mathematik Gruppe Mathematik |
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