Normal Subgroup


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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.

References in periodicals archive ?
However, while group quotients are always of the form G/N, N a normal subgroup, Hopf quotients arise from normal left coideal subalgebras which are not necessarily Hopf subalgebras.
then H is semi closed, and a normal subgroup of (Eq.
Let G be a profinite group which acts continuously and faithfully on V and let N be a closed normal subgroup of G.
The plasma renalase levels of the subgroups with multiple- branch and two-branch stenosis were significantly lower than that of the normal subgroup (Pless than 0.
If N is a normal subgroup of G, the binary operation on left cosets has the structure of a group, the quotient group G/N.
Let p be the smallest prime dividing the order of a group G and H a normal subgroup of G such that G/H is p-nilpotent.
Then, H is normal subgroup of G if gH = Hg [for all] g [member of] G.
On the other hand, given a group G with a normal subgroup N [?
Let SG be the normal subgroup of orientation preserving elements; then G/SG [approximately equal to] [Z.
Kirtland provides a handy reference for results concerning normal subgroup complementation in finite groups.
These automorphisms form a normal subgroup of Aut(G), which we denote by Autcent(G).