# Definitions for derived subgroupde·rived sub·group

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1. derived subgroupnoun

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

### WikipediaRate this definition:0.0 / 0 votes

1. derived 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.

### Numerology

1. Chaldean Numerology

The numerical value of derived subgroup in Chaldean Numerology is: 1

2. Pythagorean Numerology

The numerical value of derived subgroup in Pythagorean Numerology is: 6

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"derived subgroup." Definitions.net. STANDS4 LLC, 2024. Web. 2 Mar. 2024. <https://www.definitions.net/definition/derived+subgroup>.

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