In abstract algebra, the conjugacy problem for a group G is the decision problem of determining, given two words x and y in G, whether or not they represent the same conjugacy class in G. Abstract algebra is the subject area of Mathematics that studies Algebraic structures such as groups, rings, fields, modules In Computability theory and Computational complexity theory, a decision problem is a question in some Formal system with a yes-or-no answer depending on In Mathematics, especially Group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class
It is known that the conjugacy problem is undecidable for many classes of groups.