极小子群拟中心的有限群  

Finite Groups of Quasicentral Minimal Subgroups

作　　者：高建玲[1] 曹建基[1] GAO Jian-ling CAO Jian-ji(School of Mathematics and Computer Sciences, Shanxi Datong University, Datong 037009, Chin)

机构地区：[1]山西大同大学数学与计算机科学学院,山西大同037009

出　　处：《中北大学学报（自然科学版）》2017年第1期24-26,共3页Journal of North University of China(Natural Science Edition)

基　　金：山西大同大学青年基金资助项目(2009Q14);山西大同大学博士科研启动经费(2014-B-08)

摘　　要：利用极小阶反例,借助内幂零群的结构,分析了有限群G及其2-极大子群与3-极大子群的p阶与4阶循环子群在G中拟中心,与G的极大子群的p阶与4阶循环子群在极大子群中拟中心,分别给出了这些群的刻画.可借助这些结论来判定某些群的p-幂零性.With minimal order counter example and the structure of inner nilpotent subgroups, the finite groups were characterized in which the subgroups of order p of 2-maximal subgroups and 3-maximal subgroups and cyclic subgroups of order 4 of finite groups G were quasicentral and whose subgroups of order p and cyclic subgroups of order 4 of maximal subgroups were quasicentral in the maximal subgroups. Then, using the conclusion, the p-nilpotency of some finite groups can be solved.

关 键 词：拟中心子群 p阶子群 P-幂零群 内幂零群 

分 类 号：O152.1[理学—数学]