What does commutator subgroup mean?
Definitions for commutator subgroup
com·mu·ta·tor sub·group
This dictionary definitions page includes all the possible meanings, example usage and translations of the word commutator subgroup.
Wiktionary
commutator subgroupnoun
The subgroup of a specified group generated by the larger group's commutators.
Wikipedia
Commutator subgroup
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.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. In other words, G / N {\displaystyle G/N} is abelian if and only if N {\displaystyle N} contains the commutator subgroup of G {\displaystyle G} . So in some sense it provides a measure of how far the group is from being abelian; the larger the commutator subgroup is, the "less abelian" the group is.
Wikidata
Commutator subgroup
In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group. 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. In other words, G/N is abelian if and only if N contains the commutator subgroup. So in some sense it provides a measure of how far the group is from being abelian; the larger the commutator subgroup is, the "less abelian" the group is.
Numerology
Chaldean Numerology
The numerical value of commutator subgroup in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of commutator subgroup in Pythagorean Numerology is: 6
Translations for commutator subgroup
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"commutator subgroup." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/commutator+subgroup>.
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