A Generalization of a Power-Conjugacy Problem in Torsion-Free Negatively Curved Groups

TL;DR

This paper presents an algorithm to determine conjugacy relations between elements of quasiconvex subgroups within negatively curved torsion-free groups, advancing understanding of subgroup conjugacy problems in geometric group theory.

Contribution

It introduces a novel algorithm for deciding conjugacy between elements of quasiconvex subgroups in negatively curved torsion-free groups.

Findings

Algorithm successfully decides conjugacy in specified groups.

Extends conjugacy problem solutions to broader classes of groups.

Provides computational tools for geometric group theory applications.

Abstract

Let H and K be quasiconvex subgroups of a negatively curved torsion-free group G. We give an algorithm which decides whether an element of H is conjugated in G to an element of K.