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: reviewed
- Last edited by Jennifer Paulhus on 2022-07-18 18:28:15
- 2022-07-18 18:28:15 by Jennifer Paulhus (Reviewed)
- 2022-07-02 17:12:48 by John Jones
- 2021-06-21 06:09:56 by David Roe