(untitled) (European Journal of Pure and Applied Mathematics, 2026)
A subgroup H of a group G is said to satisfy Π-property in G such that for any G-chief factor U/V, |G/V:N_G/V(HV/VU/V)| is a π(HV/VU/V)-number. In this paper, we present a new criterion for p-supersolvability of finite groups by using of a small quantity of maximal subgroups of a Sylow p-subgroup satisfying the Π-property. As applications, we obtain some sufficient conditions for a finite group to be p-nilpotent and supersolvable. A number of known results are improved and extended.