In order for a complement to exist, the sequence $$1 \to H \to G \to G/H \to 1$$ must split, in which case the complements are precisely the images of the possible splittings $G/H \to G$. All complements are isomorphic to $G/H$, and if $K$ is any complement then $G$ can be described as the internal semidirect product $H \rtimes K$.
- Review status: beta
- Last edited by David Roe on 2021-06-21 06:09:56
Not referenced anywhere at the moment.