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Uniform Growth in Groups of Exponential Growth

Published in Geometriae Dedicata. 2002, vol. 95, no. 1, p. 1-17
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.
Keywords Exponential growthGrowth of groupsUniform exponential growth
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DE LA HARPE, Pierre. Uniform Growth in Groups of Exponential Growth. In: Geometriae Dedicata, 2002, vol. 95, n° 1, p. 1-17. https://archive-ouverte.unige.ch/unige:12370

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Deposited on : 2010-11-08

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