nLab
commutator subgroup

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Definition

For GG a group its commutator subgroup [G,G]G[G,G] \hookrightarrow G is the smallest subgroup containing all the group commutator elements [g,h]g 1h 1gh[g,h] \coloneqq g^{-1} h^{-1} g h.

This definition also makes sense for invertible semigroups, for which they would be called ‘commutator invertible subsemigroups’.

Properties

Last revised on June 14, 2021 at 11:13:20. See the history of this page for a list of all contributions to it.