The power conjugacy problem in Higman-Thompson groups

TL;DR

This paper revises Higman's original conjugacy algorithm for Higman-Thompson groups, providing a complete solution to the power conjugacy problem with explicit algorithms and Python implementations.

Contribution

It offers a corrected and complete algorithm for the power conjugacy problem in Higman-Thompson groups, improving upon Higman's original flawed approach.

Findings

Revised algorithm successfully solves the power conjugacy problem

Explicit Python implementations are provided

The corrected algorithm addresses cases where Higman's original approach failed

Abstract

An introduction to the universal algebra approach to Higman-Thompson groups (including Thompson's group $V$) is given, following a series of lectures by Graham Higman in 1973. In these talks, Higman outlined an algorithm for the conjugacy problem; which although essentially correct fails in certain cases, as we show here. A revised and complete version of the algorithm is written out explicitly. From this, we construct an algorithm for the power conjugacy problem in these groups. Python implementations of these algorithms can be found at [26].