Conjugacy problem for subgroups with applications to Artin groups and braid type groups

Abstract

Let G be a group endowed with a solution to the conjugacy problem and with an algorithm which computes the centralizer in G of any element of G. Let H be a subgroup of G. We give some conditions on H, under which we provide a solution to the conjugacy problem in H. We apply our results to some Artin groups and braid type groups. In particular, we give explicit solutions to the conjugacy problem in the Artin groups of type A~n and C~n.