Geometriae Dedicata

, Volume 95, Issue 1, pp 1–17

Uniform Growth in Groups of Exponential Growth

Authors

  • Pierre De La Harpe
    • Section de Mathématiques
Article

DOI: 10.1023/A:1021273024728

Cite this article as:
Harpe, P.D.L. Geometriae Dedicata (2002) 95: 1. doi:10.1023/A:1021273024728

Abstract

This is an exposition of examples and classes of finitely-generated groups which have uniform exponential growth. The main examples are non-Abelian free groups, semi-direct products of free Abelian groups with automorphisms having an eigenvalue of modulus distinct from 1, and Golod–Shafarevich infinite finitely-generated p-groups. The classes include groups which virtually have non-Abelian free quotients, nonelementary hyperbolic groups, appropriate free products with amalgamation, HNN-extensions and one-relator groups, as well as soluble groups of exponential growth. Several open problems are formulated.

exponential growth growth of groups uniform exponential growth

Copyright information

© Kluwer Academic Publishers 2002