Definition:Generated Normal Subgroup/Definition 1

Definition

Let $G$ be a group.

Let $S \subseteq G$ be a subset.

The normal subgroup generated by $S$, denoted $\gen {S^G}$, is the intersection of all normal subgroups of $G$ containing $S$.

Also see

• Equivalence of Definitions of Generated Normal Subgroup
• Intersection of Normal Subgroups is Normal