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Algebraic entropy of elementary amenable groups

D. V. Osin
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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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BibTeXRIS

D. V. Osin. 2004-04-05. Algebraic entropy of elementary amenable groups. https://arxiv.org/abs/math/0404075

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