#
nLab

group commutator

Contents
### Context

#### Group Theory

**group theory**

### Classical groups

### Finite groups

### Group schemes

### Topological groups

### Lie groups

### Super-Lie groups

### Higher groups

### Cohomology and Extensions

# Contents

## Definition

For $g,h \in G$ two elements of a group, their **group commutator** is defined as

$[g,h] \coloneqq g^{-1} h^{-1} g h
\,.$

This definition Is also valid for invertible semigroups.

Last revised on June 14, 2021 at 10:05:55.
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