Random subgroups of acylindrically hyperbolic groups and hyperbolic\n embeddings

2017/01/01 by Joseph Maher, Alessandro Sisto, Maher, Joseph +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1701.00253

openalex publication_date 2017/01/01 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let G be an acylindrically hyperbolic group. We consider a random subgroup H\nin G, generated by a finite collection of independent random walks. We show\nthat, with asymptotic probability one, such a random subgroup H of G is a free\ngroup, and the semidirect product of H acting on E(G) is hyperbolically\nembedded in G, where E(G) is the unique maximal finite normal subgroup of G.\n

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