How did the author get that $L=(L \cap H)(L\cap K)$ in Lemma $5$ below.
Remark: All the groups here are finite. $H$ permutes (commutes) with $K$ means $HK=KH$ where $H$ and $K$ are subgroups of some finite group $G$.
Thanks in advance.
How did the author get that $L=(L \cap H)(L\cap K)$ in Lemma $5$ below.
Remark: All the groups here are finite. $H$ permutes (commutes) with $K$ means $HK=KH$ where $H$ and $K$ are subgroups of some finite group $G$.
Thanks in advance.