On c-normal and hypercentrally embeded subgroups of finite groups

In this article, we investigate the structure of a finite group $G$ under the assumption that some subgroups of $G$ are c-normal in $G$. The main theorem is as follows:
Theorem A. Let $E$ be a normal finite group of $G$. If all subgroups of $E_{p}$ with order $d_{p}$ and 2$d_{p}$ (if $p=2$ and $E_{p}$ is not an abelian nor quaternion free 2-group) are c-normal in $G$, then $E$ is $p$-hypercyclically embedded in $G$.
We give some applications of the theorem and generalize some known results.