Abstract
A subgroup S of a group 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. The main aim of this paper is to investigate the influence of p-sylowizers on the structure of finite groups. We obtained some new characterizations of p-nilpotent and supersolvable groups by the permutability of the p-sylowizers of some p-subgroups. In addition, we determined all p-sylowizers of arbitrary p-subgroups for the supersolvable groups.
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