commutator subgroup


Also found in: Wikipedia.

commutator subgroup

[′käm·yə‚tād·ər ′səb‚grüp]
(mathematics)
The subgroup of a given group G consisting of all products of the form g1 g2gn, where each gi is the commutator of some pair of elements in G.
Mentioned in ?
References in periodicals archive ?
ij] [member of] Z and M' is in the commutator subgroup of [[GAMMA].
Let G be a finite group and G' its commutator subgroup.
The subgroup of G generated by the set {[x, y]| x, : y [member of] G} is called the commutator subgroup of G and will be denoted G'.
Also, Pettet gave a more general statement proving that A(G) = 1 if Z(G) = 1 and the commutator subgroup [[gamma].
ab] be the maximal abelian covering over X corresponding to the commutator subgroup [[[pi].
For a group X, let X' be the commutator subgroup of X.