Introduction to group theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German English Russian |
| Published: |
Zürich
European Math. Soc.
2008
|
| Series: | EMS textbooks in mathematics
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 177 S. Ill., graph. Darst. |
| ISBN: | 9783037190418 3037190418 |
Staff View
MARC
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| 100 | 1 | |a Bogopol'skij, Oleg V. |e Verfasser |0 (DE-588)140917632 |4 aut | |
| 240 | 1 | 0 | |a Vvedenie v teoriju grupii |
| 245 | 1 | 0 | |a Introduction to group theory |c Oleg Bogopolski |
| 264 | 1 | |a Zürich |b European Math. Soc. |c 2008 | |
| 300 | |a X, 177 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a EMS textbooks in mathematics | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Combinatorial group theory | |
| 650 | 4 | |a Finite groups | |
| 650 | 4 | |a Group theory | |
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Record in the Search Index
| _version_ | 1805090664817360896 |
|---|---|
| adam_text |
Contents
Preface
v
Preface
to the Russian Edition
vi
1
Introduction to finite group theory
1
1
Main definitions
. 1
2
Lagrange's theorem. Normal subgroups and factor groups
. 4
3
Homomorphism theorems
. 6
4
Cayley's theorem
. 7
5
Double cosets
. 9
6
Actions of groups on sets
. 10
7
Normalizers and centralizers. The centers of finite p-groups
. 12
8
Sylow's theorem
. 13
9
Direct products of groups
. 15
10
Finite simple groups
. 16
11
The simplicity of the alternating group An for
η
> 5 . 18
12
As as the rotation group of an icosahedron
. 19
13
As as the first noncyclic simple group
. 20
14
As as a projective special linear group
. 22
15
A theorem of Jordan and
Dickson
. 23
16
Mathieu's group
Міг
. 25
17
The
Mathieu
groups,
Steiner
systems and coding theory
. 32
18
Extension theory
. 35
19
Schur's theorem
. 37
20
The Higman-Sims group
. 39
2
Introduction to combinatorial group theory
45
1
Graphs and Cayley's graphs
. 45
2
Automorphisms of trees
. 50
3
Free groups
. 52
4
The fundamental group of a graph
. 56
5
Presentation of groups by generators and relations
. 58
6
Tietze transformations
. 60
7
A presentation of the group Sn
. 63
8
Trees and free groups
. 64
9
The rewriting process of Reidemeister-Schreier
. 69
10
Free products
. 71
11
Amalgamated free products
. 72
X
Contents
12
Trees and amalgamated free products
. 74
13
Action of the group SL2(Z) on the hyperbolic plane
. 76
14
HNN extensions
. 81
15
Trees and HNN extensions
. 84
16
Graphs of groups and their fundamental groups
. 84
17
The relationship between amalgamated products
and HNN extensions
. 87
18
The structure of a group acting on a tree
. 88
19
Kurosh's theorem
. 92
20
Coverings of graphs
. 93
21
S
-graphs and subgroups of free groups
. 96
22
Foldings
. 98
23
The intersection of two subgroups of a free group
. 101
24
Complexes
. 104
25
Coverings of complexes
. 106
26
Surfaces
. 109
27
The theorem of
Seifert
and van
Kampen. 115
28
Grushko's Theorem
. 115
29
Hopfian groups and residually finite groups
. 117
3
Automorphisms of free groups and train tracks
121
1
Nielsen's method and generators of Aut(Fn)
. 123
2
Maps of graphs. Tightening, collapsing and expanding
. 126
3
Homotopy equivalences
. 128
4
Topological representatives
. 129
5
The transition matrix. Irreducible maps and automorphisms
. 130
6
Train tracks
. 132
7
Transformations of maps
. 132
8
The metric induced on a graph by an irreducible map
. 137
9
Proof of the main theorem
. 138
10
Examples of the construction of train tracks
. 141
11
Two applications of train tracks
. 151
Appendix. The Perron-Frobenius Theorem
153
Solutions to selected exercises
157
Bibliography
169
Index
173 |
| adam_txt |
Contents
Preface
v
Preface
to the Russian Edition
vi
1
Introduction to finite group theory
1
1
Main definitions
. 1
2
Lagrange's theorem. Normal subgroups and factor groups
. 4
3
Homomorphism theorems
. 6
4
Cayley's theorem
. 7
5
Double cosets
. 9
6
Actions of groups on sets
. 10
7
Normalizers and centralizers. The centers of finite p-groups
. 12
8
Sylow's theorem
. 13
9
Direct products of groups
. 15
10
Finite simple groups
. 16
11
The simplicity of the alternating group An for
η
> 5 . 18
12
As as the rotation group of an icosahedron
. 19
13
As as the first noncyclic simple group
. 20
14
As as a projective special linear group
. 22
15
A theorem of Jordan and
Dickson
. 23
16
Mathieu's group
Міг
. 25
17
The
Mathieu
groups,
Steiner
systems and coding theory
. 32
18
Extension theory
. 35
19
Schur's theorem
. 37
20
The Higman-Sims group
. 39
2
Introduction to combinatorial group theory
45
1
Graphs and Cayley's graphs
. 45
2
Automorphisms of trees
. 50
3
Free groups
. 52
4
The fundamental group of a graph
. 56
5
Presentation of groups by generators and relations
. 58
6
Tietze transformations
. 60
7
A presentation of the group Sn
. 63
8
Trees and free groups
. 64
9
The rewriting process of Reidemeister-Schreier
. 69
10
Free products
. 71
11
Amalgamated free products
. 72
X
Contents
12
Trees and amalgamated free products
. 74
13
Action of the group SL2(Z) on the hyperbolic plane
. 76
14
HNN extensions
. 81
15
Trees and HNN extensions
. 84
16
Graphs of groups and their fundamental groups
. 84
17
The relationship between amalgamated products
and HNN extensions
. 87
18
The structure of a group acting on a tree
. 88
19
Kurosh's theorem
. 92
20
Coverings of graphs
. 93
21
S
-graphs and subgroups of free groups
. 96
22
Foldings
. 98
23
The intersection of two subgroups of a free group
. 101
24
Complexes
. 104
25
Coverings of complexes
. 106
26
Surfaces
. 109
27
The theorem of
Seifert
and van
Kampen. 115
28
Grushko's Theorem
. 115
29
Hopfian groups and residually finite groups
. 117
3
Automorphisms of free groups and train tracks
121
1
Nielsen's method and generators of Aut(Fn)
. 123
2
Maps of graphs. Tightening, collapsing and expanding
. 126
3
Homotopy equivalences
. 128
4
Topological representatives
. 129
5
The transition matrix. Irreducible maps and automorphisms
. 130
6
Train tracks
. 132
7
Transformations of maps
. 132
8
The metric induced on a graph by an irreducible map
. 137
9
Proof of the main theorem
. 138
10
Examples of the construction of train tracks
. 141
11
Two applications of train tracks
. 151
Appendix. The Perron-Frobenius Theorem
153
Solutions to selected exercises
157
Bibliography
169
Index
173 |
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| spelling | Bogopol'skij, Oleg V. Verfasser (DE-588)140917632 aut Vvedenie v teoriju grupii Introduction to group theory Oleg Bogopolski Zürich European Math. Soc. 2008 X, 177 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Aus dem Russ. übers. Combinatorial group theory Finite groups Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Gruppentheorie (DE-588)4072157-7 s DE-604 Erscheint auch als ebook Bogopol'skij, Oleg V. Introduction to group theory 978-3-03719-541-3 (DE-604)BV036713243 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3078001&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016552509&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bogopol'skij, Oleg V. Introduction to group theory Combinatorial group theory Finite groups Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4151278-9 |
| title | Introduction to group theory |
| title_alt | Vvedenie v teoriju grupii |
| title_auth | Introduction to group theory |
| title_exact_search | Introduction to group theory |
| title_exact_search_txtP | Introduction to group theory |
| title_full | Introduction to group theory Oleg Bogopolski |
| title_fullStr | Introduction to group theory Oleg Bogopolski |
| title_full_unstemmed | Introduction to group theory Oleg Bogopolski |
| title_short | Introduction to group theory |
| title_sort | introduction to group theory |
| topic | Combinatorial group theory Finite groups Group theory Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Combinatorial group theory Finite groups Group theory Gruppentheorie Einführung |
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