ON WEAKLY $A\mathcal{H}$-SUBGROUPS OF FINITE GROUPS

An $A$-invariant subgroup $H$ of a finite group $G$ is called weakly $A\mathcal{H}$-subgroup of $G$ if there exists an $A$-invariant normal subgroup $K$ of $G$ such that $G=HK$ and $H\cap K\in \mathcal{H}(G)$, where $\mathcal{H}(G)$ is the set of all $\mathcal{H}$-subgroups of a group $G$. In this paper, we obtain some results on weakly $A\mathcal{H}$-subgroups and by using these results, we are able to determine the structures of some groups.