Let $\displaystyle G$ be a finite group. Let $\displaystyle H$ and $\displaystyle K$ be normal $\displaystyle p$-subgroups of $\displaystyle G$ for some prime $\displaystyle p$ with $\displaystyle H$ being a proper subgroup of $\displaystyle K$ and $\displaystyle H/K$ is elementary abelian p-group. Let $\displaystyle S$ be a normal subgroup of $\displaystyle K$ with $\displaystyle H<S$. If $\displaystyle H$ contain every element of order $\displaystyle p$ of $\displaystyle S$ and$\displaystyle K=<S^{g},g \in G>$, then $\displaystyle H$ contain every element of order $\displaystyle p$ of $\displaystyle K$.

I need to prove the above statement. Thanks in advance.