U-可补子群与有限群的p-幂零性

华东师范大学学报(自然科学版) ›› 2011, Vol. 2011 ›› Issue (5): 88-92.

U-可补子群与有限群的p-幂零性

李长稳, 胡滨

徐州师范大学数学科学学院, 徐州 221116

收稿日期:2010-10-01 修回日期:2011-01-01 出版日期:2011-09-25 发布日期:2011-11-22

U-supplemented subgroups and p-nilpotency of finite groups

LI Chang-wen, HU Bin

School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China

Received:2010-10-01 Revised:2011-01-01 Online:2011-09-25 Published:2011-11-22

摘要/Abstract

摘要： 研究了U-可补子群对有限群结构的影响. 在一些准素子群(例如, Sylow子群的2-极大子群)U-可补的假设下, 一些p-幂零性的条件被建立, 同时得到了一个群属于给定的有限群的群系的新的刻画. 作为应用, 推广和统一了一些已知的结果.

关键词: U-可补, p-幂零, Sylow p-子群

Abstract: The influence of U-supplemented subgroups on the structure of finite groups was investigated. Some conditions of p-nilpotency under assumption that some primary subgroups (for example, 2-maximal subgroups of Sylow subgroup) are U-supplemented were established. Meanwhile, some new characterizations of a group belonging to a given formation of finite groups were obtained. As an application, a series of previously known results are unified and generalized.

Key words: U-supplemented, p-nilpotent, Sylow p-subgroup

中图分类号:

O512

李长稳, 胡滨. U-可补子群与有限群的p-幂零性[J]. 华东师范大学学报(自然科学版), 2011, 2011(5): 88-92.

LI Chang-wen, HU Bin. U-supplemented subgroups and p-nilpotency of finite groups[J]. Journal of East China Normal University(Natural Sc, 2011, 2011(5): 88-92.