Geometriae Dedicata

, Volume 95, Issue 1, pp 1–17

Uniform Growth in Groups of Exponential Growth

  • Pierre De La Harpe


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 


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© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Pierre De La Harpe
    • 1
  1. 1.Section de MathématiquesGenève 24Switzerland

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