Semi-Cover-Avoiding Properties and the Structure of Finite Groups

DOI：10.3770/j.issn:1000-341X.2010.03.017

 作者 单位 王俊新 山西财经大学数学系, 山西 太原 030006 郭秀云 上海大学数学系, 上海 200444

本文定义和研究了子群的半$\pi$-覆盖远离性质,并利用该性质刻划了有限群的$\pi$-可解性.其他若干关于某些子群的半覆盖远离性与有限群结构的关系定理也被得到.

In this paper, the so-called $\pi$-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the $\pi$-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.