Let $H, K\leq G$. I was wondering what you call the "product" $HK$ of $H$ and $K$.
I was trying to verbalise the steps of showing $G$ is a semidirect product:
Normality of $H$: $H\unlhd G$.
Trivial intersection: $H\cap K=1$.
However, I feel that there has to be a better word than "product" here.
Is there a "correct" answer? If so, I would appreciate it if you were to tell me what this answer is...