A note on p-supersolubility of finite groups

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