Conjugacy class

In group theory, equivalence class under the relation of conjugation

In mathematics, especially group theory, two elements a {\displaystyle a} and b {\displaystyle b} of a group are conjugate if there is an element g {\displaystyle g} in the group such that b = g a g − 1 . {\displaystyle b=gag^{-1}.} This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under the maps a ↦ g a g − 1 , {\displaystyle a\mapsto gag^{-1},} with g {\displaystyle g} an element of the group.

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