nLab
commutator subgroup

Contents

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.

Properties

Last revised on August 31, 2012 at 21:07:39. See the history of this page for a list of all contributions to it.