(p-)hereditary conjugacy separability in graph products of groups and applications Seminar

Groups can be quite complicated. Sometimes we would like to know how much of information about a given group can we reconstruct from its finite quotients. For example: suppose we are given two groups elements and we know that their images are not conjugate in all finite quotients, is it enough to conclude that they are not conjugate in the given group? Groups with this property are called conjugacy separable (CS).

It is natural to ask by which group constructions is this property preserved. We give a hint of a proof that the class of (p)HCS groups is closed under graph products and we show some application.