The semi p-cover-avoidance properties of p-sylowizers in finite groups

Abstract

A subgroup S of G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. In this paper, we give some new characterizations of p-solvable and p-supersolvable groups by the p-cover-avoidance properties of the p-sylowizers of some p-subgroups and the p-sylowizers in some classes of groups.