On the $p$-supersolubility of a finite group with a $\mu$-supplemented Sylow $p$-subgroup

A subgroup $H$ of a group $G$ is called $\mu$-supplemented in $G$ if there exists a subgroup $K$ such that $G=HK$ and $H_1K$ is a proper subgroup in $G$ for every maximal subgroup $H_1$ in $H$. For the initial values of $p$, we establish the $p$-supersolubility of a finite group with a $\mu$-supplemented Sylow $p$-subgroup.