# Conjugacy

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In group theory, **conjugacy** is the relation between elements of a group that states that one element is the conjugate of the other. This relation is an equivalence relation, and the equivalence classes are the **conjugacy classes** of the group.

Another way of stating this is to say that conjugation is group action of *G* on itself, and the conjugacy classes are the orbits of this action.

The **conjugacy problem** is the decision problem of determining from a presentation of a group whether two elements of the group are conjugate .

The conjugacy problem was identified by Max Dehn in 1911 as one of three fundamental decision problems in group theory; the other two being the group isomorphism problem and the word problem.