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MAA Reviews

How Groups Grow

Avinoam Mann

Table of Contents

Preface
1. Introduction
2. Some group theory
3. Groups of linear growth
4. The growth of nilpotent groups
5. The growth of soluble groups
6. Linear groups
7. Asymptotic cones
8. Groups of polynomial growth
9. Infinitely generated groups
10. Intermediate growth: Grigorchuk's first group
11. More groups of intermediate growth
12. Growth and amenability
13. Intermediate growth and residual finiteness
14. Explicit calculations
15. The generating function
16. The growth of free products
17. Conjugacy class growth
Research problems
References.

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