On the existence of weakly malnormal quasiconvex subgroups of hyperbolic groups

TL;DR

This paper proves that every nonelementary hyperbolic group contains weakly malnormal, virtually free, quasiconvex subgroups, extending previous results about malnormal quasiconvex subgroups in torsion-free cases.

Contribution

It establishes the existence of weakly malnormal, quasiconvex subgroups in all nonelementary hyperbolic groups, broadening the scope of known subgroup structures.

Findings

Existence of weakly malnormal quasiconvex subgroups in any nonelementary hyperbolic group

Extension of Kapovich's result from torsion-free to all hyperbolic groups

Broadening understanding of subgroup configurations in hyperbolic groups

Abstract

In this short note, we prove the existence of weakly malnormal, virtually free, quasiconvex subgroups in any nonelementary hyperbolic group. This extends a result of Ilya Kapovich, where he proved the existence of malnormal quasiconvex subgroups in torsion-free hyperbolic groups.