Conjugacy problem (original) (raw)

In abstract algebra, the conjugacy problem for a group G with a given presentation is the decision problem of determining, given two words x and y in G, whether or not they represent conjugate elements of G. That is, the problem is to determine whether there exists an element z of G such that The conjugacy problem is also known as the transformation problem. It is known that the conjugacy problem is undecidable for many classes of groups.Classes of group presentations for which it is known to be soluble include: