极小子群及4阶循环子群的半覆盖远离性

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (3): 268-271.

极小子群及4阶循环子群的半覆盖远离性

张方锁,郭秀云

(上海大学理学院,上海 200444)

出版日期:2010-06-28 发布日期:2010-06-28

Minimal Subgroups and Cyclic Subgroups of Order 4 with Semi-Cover-Avoiding Property

ZHANG Fang-suo,GUO Xiu-yun

(College of Sciences,Shanghai University,Shanghai 200444,China)

Online:2010-06-28 Published:2010-06-28

摘要/Abstract

摘要：

群G的一个子群H称为在G中具有半覆盖远离性,如果存在G的一个主群列1=G₀1<…l=G,使得对每一个j=1,2,…,l,或者H覆盖Gj/Gj－1,或者H远离Gj/Gj－1.利用极小子群及4阶循环子群具有半覆盖远离性的性质,得到一些新的关于有限群为幂零群或超可解群的充分必要条件，推广了以前的结论.

Abstract:

A subgroup H is said to be semi-cover-avoiding in a group G if there is a chief series 1=G₀1<…l=G such that for every j=1,2,…,l, either H covers Gj/Gj－1 or H avoids Gj/Gj－1. In this paper, some new necessary and sufficient conditions for a finite group G to be nilponent or supersolvable are given by using minimal subgroups and cyclic subgroups of order 4 with semi-cover-avoiding property in the group. Some known results are generalized. 

Key words: semi-cover-avoiding property; minimal subgroup; nilpotent group; supersolvble group; supersolvble embedding group

张方锁,郭秀云. 极小子群及4阶循环子群的半覆盖远离性[J]. 上海大学学报(自然科学版), 2010, 16(3): 268-271.

ZHANG Fang-suo,GUO Xiu-yun. Minimal Subgroups and Cyclic Subgroups of Order 4 with Semi-Cover-Avoiding Property[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(3): 268-271.