关于有限群的p-恩格尔元

On p-Engel elements of finite groups

本文引入有限群恩格尔元的一个推广概念——p-恩格尔元,探讨了p-恩格尔元及其相关集合的基本性质并利用p-恩格尔元的概念,得到有限群成为p-闭群的几个充分或必要条件以及可解内p-闭群的几个集合的一个刻画。

This paper introduces a generalization of the concept of Engel elements called p-Engel elements,and investigates some basic properties of p-Engel elements together with some related sets.By using the concept of p-Engel elements,a description of several sufficient or necessary conditions for a finite group to be p-close and a characterization on several sets of a soluble inner p-closed group are obtained.