A result on s-semipermutable subgroups of finite groups and some applications

Abstract

–Let p be a prime number, G be a p-solvable finite group and P be a Sylow p-subgroup of G. We prove that G is p-supersolvable if is p-supersolvable and if there is a subgroup H of P with such that H is s-semipermutable in G. As applications, we simplify the proofs of some known results and also generalize some known results.