# Normal Subgroup

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Related to Normal Subgroup: Quotient group, Commutator subgroup, Center of a group, Index of a subgroup

## normal subgroup

[′nȯr·məl ′səb‚grüp] (mathematics)

A subgroup

*N*of a group*G*where every expression*g*^{-1}*ng*is in*N*for every*g*in*G*and every*n*in*N*. Also known as invariant subgroup; normal divisor.## Normal Subgroup

(also normal divisor of a group, invariant subgroup), a fundamental concept of group theory, which was introduced by E. Galois. A normal subgroup of a group *G* is a subgroup *H* for which *gH = Hg* for arbitrary element *g* of group *G*.