Definition:Conjugate (Group Theory)/Subset/Also defined as

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Definition

Let $\struct {G, \circ}$ be a group.

Let $S \subseteq G, a \in G$.


The $G$-conjugate of $S$ by $a$ is:

$S^a := \set {y \in G: \exists x \in S: y = a^{-1} \circ x \circ a} = a^{-1} \circ S \circ a$


Also see


Sources