p-sylowizers and p-nilpotency of finite groups

TL;DR

This paper studies the structure of finite groups by examining p-sylowizers and their intersections with certain subgroups, providing new criteria for p-nilpotency based on subgroup permutability conditions.

Contribution

It introduces novel criteria for p-nilpotency of finite groups using intersections of p-sylowizers and S-permutability conditions.

Findings

Established new p-nilpotency criteria based on subgroup intersections.

Linked p-sylowizer properties to group structure and permutability.

Provided conditions for p-nilpotency in finite groups.

Abstract

In this paper, we investigate the structure of finite group G by assuming that the intersections between p-sylowizers of some p-subgroups of G and $O^p(G)$ are S-permutable in G. We obtain some criterions for p-nilpotency of a finite group.