How Groups Grow

Avinoam Mann is a Professor Emeritus at his Alma Mater, the Einstein Institute of Mathematics in the Hebrew University of Jerusalem. He has published over a hundred papers on group theory and co-authored the influential book Analytic Pro-p Groups.

• 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.

'How Groups Grow is an excellent introduction to growth of groups for everybody interested in this subject. It also touches a variety of adjacent subjects (such as amenability, isoperimetric inequalities, groups generated by automata, etc.) It is written in a very accessible style, with very clear exposition of all main results.' V. Nekrashevych, Bulletin of the American Mathematical Society