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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]
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.
(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.