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

Revised on August 31, 2012 21:07:39 by Ingo Blechschmidt (46.244.128.155)