Definition:Generated Normal Subgroup/Definition 2

Definition

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Let $G$ be a group.

Let $S \subseteq G$ be a subset.

The normal subgroup generated by $S$, denoted $\gen {S^G}$, is the smallest normal subgroup of $G$ containing $S$:

$\gen {S^G} = \gen {x S x^{-1}: x \in G}$

Also see

• Equivalence of Definitions of Generated Normal Subgroup

Sources

• 1967: John D. Dixon: Problems in Group Theory ... (previous) ... (next): Introduction: Notation