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Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings

· 2017 · math.GT · arXiv 1701.00253

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abstract

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

fields

math.GR 1

years

2019 1

verdicts

UNVERDICTED 1

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Random subgroups, automorphisms, splittings

math.GR · 2019-06-23 · unverdicted · novelty 6.0

Random subgroups of free groups and groups hyperbolic relative to slender subgroups are invariant only under inner automorphisms.

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  • Random subgroups, automorphisms, splittings math.GR · 2019-06-23 · unverdicted · none · ref 12 · internal anchor

    Random subgroups of free groups and groups hyperbolic relative to slender subgroups are invariant only under inner automorphisms.