Conjugate (group theory)

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Let $G$ be a group operating on a set $S$. An element $y\in S$ conjugate to an element $x\in S$ if there exists an element $\alpha \in G$ such that $y = \alpha x$. The relation of conjugacy is an equivalence relation. The set of conjugates of an element $x$ of $S$ is called the orbit of $x$.

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