Contents

group theory

# Contents

## Definition

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

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.