Definition: Conjugate Elements of a Group

Let $(G,\ast)$ be a group. Two elements $a,b\in G$ are called conjugate if there exists an element $h\in G$ with $$a=h^{-1}\ast b\ast h.$$ In this case, conjugate elements are denoted by $a\sim_G b.$ If the context of the group is clear, then we write $a\sim b.$

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