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Actions of maximal growth of hyperbolic groups

2012/01/06 by V. V. Chaynikov, Vladimir Chaynikov, Chaynikov, Vladimir
Computer Science · Mathematics · #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1201.1349

19 pages, 2 figures

openalex publication_date 2012/01/06 · arxiv created 2012/02/08 · arxiv updated 2012/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every non-elementary hyperbolic group G acts with maximal growth on some set X such that every orbit of any element g ∈ G is finite. As a side-product of our approach we prove that if G is non-elementary hyperbolic, \HH ≤ G is quasiconvex of infinite index then there exists g ∈ G such that <\HH,g> is quasiconvex of infinite index and is isomorphic to \HH*<g > if and only if \HH ∩ E(G)= \e\ , where E(G) is the maximal finite normal subgroup of G.

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