Definition:Normal Subset/Definition 3

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Definition

Let $\left({G, \circ}\right)$ be a group.

Let $S \subseteq G$ be a general subset of $G$.


Then $S$ is a normal subset of $G$ iff:

$\forall g \in G: g \circ S \circ g^{-1} \subseteq S$

or, equivalently:

$\forall g \in G: g^{-1} \circ S \circ g \subseteq S$


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