commutator subgroup

noun

The subgroup of a specified group generated by the larger group's commutators.

“The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian.^([wikipedia])”

Similar
derived groupderived subgroup
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Meanings

nouncommutator subgroup (plural commutator subgroups)

plural commutator subgroups

  1. algebraThe subgroup of a specified group generated by the larger group's commutators.

    The commutator subgroup is important because it is the smallest normal subgroup such that the quotient group of the original group by this subgroup is abelian.^([wikipedia])

    Synonyms: derived group, derived subgroup

Synonyms & antonyms

nounThe subgroup of a specified group generated by the larger group's commutators.

Similar
derived groupderived subgroup
Also see
derived groupderived subgroup
Cite this entry
APA

commutator subgroup. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/commutator%20subgroup

MLA

“commutator subgroup.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/commutator%20subgroup. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “commutator subgroup,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/commutator%20subgroup.

Source: commutator subgroup on Wiktionary, CC BY-SA 4.0.