4 of 5 added 21 characters in body

The group $G\cong H\times K$ with $H\cong \langle S_H\mid R_H\rangle$ and $K\cong \langle S_K\mid R_K\rangle$ has as a presentation $$G\cong \langle S_H\cup S_K\mid R_H\cup R_K\cup X\rangle,$$ where $X=\{hk=kh\mid h\in S_H\text{ and } k\in S_K\}$, from which it is easy to see that $H\cong L$ such that $L\unlhd G$. (Why?)