Good afternoon everyone, I need a little verification, I don't want to post it as question, if would be nice if any of you verify the following and message me, thanks:
this is from Zassenhaus Lemma.Let $H', H, K',$ and $K$ be subgroups
of a group $G$ such that H' is a normal subgroup of $H$ and $K'$ is a normal
subgroup of $K$. Set $J = (H \cap K')(H' \cap K)$. Define the function $f: H'(H\cap K) \rightarrow (H\cap K)/J$ as follows: If $a \in H'(H\cap K)$, then $a = h'b$, where $h' \in H'$ and $b \in H \cap K$. Set $f(a)=Jb$. it is already proven that the function $f$ is well defined and a…