An Algorithm to Solve the Generalized Conjugacy Problem in Relatively Hyperbolic Groups

TL;DR

This paper presents a super-exponential time algorithm for solving the generalized conjugacy problem in relatively hyperbolic groups, assuming solvability in their parabolic subgroups, advancing computational group theory.

Contribution

It introduces a novel algorithm that extends solutions to the conjugacy problem from parabolic subgroups to the entire relatively hyperbolic group.

Findings

Algorithm solves the generalized conjugacy problem in super-exponential time.

Assumes solvability of the problem in parabolic subgroups.

Provides a method to extend solutions from subgroups to the whole group.

Abstract

In this note, we provide a (super-exponential time) algorithm to solve the generalized conjugacy problem in relatively hyperbolic groups, given solvability of the generalized conjugacy problem in each of the parabolic subgroups.