A note on a result of Aseeri and Kaspczyk about p-supersolvability of finite groups

Abstract

Let G be a p-solvable finite group, where p is a prime dividing the order of G, and P be a Sylow p-subgroup of G. In this short note, we prove that the p-length of G is 1 if there is a subgroup H of P with such that H is s-semipermutable or s-permutably embedded in G. Our result not only simplifies, but also generalizes some main theorems of Aseeri and Kaspczyk [A result on s-semipermutable subgroups of finite groups and some applications, Commun. Algebra (2023)].