commutator subgroup


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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.
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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'.
Topics covered include counting of subgroups and proof of the main counting theorems, regular p-groups and regularity criteria, p-groups of maximal class and their characterizations, characters of p-groups, p-groups with large Schur multiplier and commutator subgroups, (p--1)- admissible Hall chains in normal subgroups, powerful p-groups, automorphisms of p-groups, p-groups that have nonnormal subgroups that are all cyclic, and Alberin's problem of abelian subgroups of small index.