A note on $p$-supersolubility of finite groups

Let $H$ be a subgroup of a finite group $G$. We say that $H$ satisfies $\mathcal{L}$-$\mathrm{\Pi }$-property in $G$ if $\mathrm{\mid }G\mathrm{/}K:N_{G\mathrm{/}K}(HK\mathrm{/}K)\mathrm{\mid }$ is a $\pi (HK\mathrm{/}K)$-number for all maximal $G$-invariant subgroup $K$ of $H^G$. In this paper, we give a characterization of finite $p$-supersoluble groups under assumption that some subgroups of prime power order satisfy $\mathcal{L}$-$\mathrm{\Pi }$-property.