# Commutator subgroup

From Maths

## Definition

Let [ilmath]C[/ilmath] be the group generated by the set of all commutators of a group [ilmath](G,\times)[/ilmath]. Then [ilmath]C[/ilmath] is a sugroup of [ilmath]G[/ilmath], furthermore it is a normal subgroup. That is to say:

- [math]C=\langle\{[g,h]\in G\ |\ g,h\in G\}\rangle[/math]

TODO: Finish page