Uniform Growth in Groups of Exponential Growth |
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Authors: | Pierre De La Harpe |
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Institution: | (1) Section de Mathématiques, CP 240, CH-1211 Genève 24, Switzerland |
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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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Keywords: | exponential growth growth of groups uniform exponential growth |
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