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 $\tilde Q$. This is equivalent to the existence of a section of the quotient map $G \to Q$.
If no such subgroup $\tilde Q$ exists, then $G$ is a non-split extension of $Q$ by $N$.
- Review status: beta
- Last edited by David Roe on 2020-12-08 01:08:58
Not referenced anywhere at the moment.