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.

Keywords:

• $\mathit{p}\mathfrak{U}$-hypercentre
• p-cover-avoidance properties
• p-solvable
• p-supersolvable
• p-sylowizer

2021 AMS Subject Classifications:

• 20D10
• 20D20

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant N. 11871360).