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Algebraic Entropy of Elementary Amenable Groups

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Abstract

We prove that any finitely generated elementary amenable group of zero (algebraic) entropy contains a nilpotent subgroup of finite index or, equivalently, any finitely generated elementary amenable group of exponential growth is of uniformly exponential growth. We also show that 0 is an accumulation point of the set of entropies of elementary amenable groups.

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Authors and Affiliations

  1. Department of Mathematics, SC 1326, Vanderbilt University, Nashville, TN 37240, U.S.A.

    D. V. Osin

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Osin, D.V. Algebraic Entropy of Elementary Amenable Groups. Geometriae Dedicata 107, 133–151 (2004). https://doi.org/10.1007/s10711-003-3497-6

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