  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].
