Random subgroups of acylindrically hyperbolic groups and hyperbolic embeddings

Joseph Maher*, Alessandro Sisto

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


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. Furthermore, with control on the lengths of the generators, we show that H satisfies a small cancellation condition with asymptotic probability one.

Original languageEnglish
Pages (from-to)3941-3980
Number of pages40
JournalInternational Mathematics Research Notices
Issue number13
Early online date10 Oct 2017
Publication statusPublished - Jul 2019

ASJC Scopus subject areas

  • Mathematics(all)


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