Given a group with elements A and X, there must be an element B which is a similarity transformation of A, B = X^(-1) A X so A and B are conjugate with respect to X. Conjugate elements have the following properties: 1. Every element is conjugate with itself. 2. If A is conjugate with B with respect to X, then B is conjugate to A with respect to X. 3. If A is conjugate with B and C, then B and C are conjugate with each other.

conjugacy class | conjugate elements | conjugate subgroup | similarity transformation | similar matrices