On sylowizers in finite p -soluble groups

摘要

In general, given a finite group G, a prime p and a p-subgroup R of G, the sylowizers of R in G are not conjugate. In this paper we afford some conditions to achieve the conjugation of the sylowizers of R in a p-soluble group G, among others 1. p = 2 and the Sylow 2-subgroups of G are dihedral or quaternion. 2. The Sylow p-subgroups of G have order at most p 3. 3. p is odd, R is abelian and every element of order p in C _G (R) lies in R.