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Uniform Growth in Groups of Exponential Growth

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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.

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  1. Section de Mathématiques, CP 240, CH-1211, Genève 24, Switzerland

    Pierre De La Harpe

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Harpe, P.D.L. Uniform Growth in Groups of Exponential Growth. Geometriae Dedicata 95, 1–17 (2002). https://doi.org/10.1023/A:1021273024728

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