دانلود کتاب How Groups Grow

فهرست مطالب :

Cover......Page 1
LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES......Page 2
Title......Page 4
Copyright......Page 5
Contents......Page 6
Preface......Page 8
1
Introduction......Page 12
2.1 Finite Index Subgroups......Page 26
2.2 Growth......Page 29
2.3 Soluble and Polycyclic Groups......Page 36
2.4 Nilpotent Groups......Page 38
2.5 Isoperimetric Inequalities......Page 43
3.1 Linear Growth......Page 47
3.2 Linear Growth Functions......Page 52
4.1 Polynomial Growth of Nilpotent Groups......Page 55
4.2 Groups of Small Degree......Page 61
5.1 Soluble Groups of Polynomial Growth......Page 67
5.2 Uniform Exponential Growth of Soluble Groups......Page 71
6
Linear Groups......Page 74
7
Asymptotic Cones......Page 78
8
Groups of Polynomial Growth......Page 88
9
Infinitely Generated Groups......Page 92
10
Intermediate Growth: Grigorchuk’s
First Group......Page 101
11.1 The General Grigorchuk Groups......Page 119
11.2 Groups Acting on Regular Trees......Page 124
11.3 Groups Defined by Finite Automata......Page 126
11.4 Bartholdi–Erschler Groups......Page 130
12.1 Amenability and Intermediate Growth......Page 132
12.2 More Isoperimetric Inequalities......Page 138
13
Intermediate Growth and
Residual Finiteness......Page 142
14.1 The Trefoil Group......Page 147
14.2 Wreath Products......Page 150
14.3 Free Products with Amalgamations and HNN-Extensions......Page 152
14.4 Central Products......Page 157
15
The Generating Function......Page 159
16
The Growth of Free Products......Page 169
17
Conjugacy Growth......Page 187
18
Research Problems......Page 196
References......Page 198
Index......Page 206