On the quasiconvexity of the fixed subgroup of endomorphisms of relatively hyperbolic groups

TL;DR

This paper proves that the fixed subgroup of a symmetric endomorphism with a relatively quasiconvex image in a finitely generated relatively hyperbolic group is itself relatively quasiconvex, advancing understanding of subgroup structures.

Contribution

It establishes the quasiconvexity of fixed subgroups under certain endomorphisms in relatively hyperbolic groups, a novel result in geometric group theory.

Findings

Fixed subgroup is relatively quasiconvex

Endomorphism with relatively quasiconvex image

Advances subgroup structure understanding in hyperbolic groups

Abstract

We prove that for any finitely generated relatively hyperbolic group G and any symmetric endomorphism f of G with relatively quasiconvex image, Fixf is relatively quasiconvex subgroup of G.