If $G$ has a subgroup $\tilde Q\leq G$ such that $\tilde Q\cap N=\langle e\rangle$, and $\tilde QN=G$, then $\tilde Q\cong Q$ and $G$ is a semidirect product of $N$ and $\tilde Q$.
If no such subgroup $\tilde Q$ exists, then $G$ is a non-split extension of $Q$ by $N$.
- Review status: beta
- Last edited by John Jones on 2019-06-12 14:47:17
Not referenced anywhere at the moment.