Source: wikibot/normal-closure-group-theory
= Normal closure (group theory)
{wiki=Normal_closure_(group_theory)}
In group theory, the concept of normal closure is related to the idea of normal subgroups. Given a group \\( G \\) and a subset \\( H \\) of \\( G \\), the normal closure of \\( H \\) in \\( G \\), denoted by \\( \\langle H \\rangle^G \\) or sometimes \\( \\langle H \\rangle^n \\), is the smallest normal subgroup of \\( G \\) that contains the set \\( H \\).