Algebraic entropy of elementary amenable groups

2004/04/05 by Denis Osin, D. V. Osin, Osin, D. V.
Mathematics · #20F65 #20F69 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #msc:20F65 #msc:20F69

paper · pdf · doi:10.48550/arxiv.math/0404075

20 pages; to appear in Geom. Dedicata

arxiv created 2004/04/05 · openalex publication_date 2004/04/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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