π-拟幂零群的极小子群与超可解性  

Minimal subgroups and supersolvabllity of π - quasinilpotent group

作　　者：陈维红[1] 诸秉政[1] 

机构地区：[1]哈尔滨师范大学阿城学院,黑龙江阿城150301

出　　处：《黑龙江大学自然科学学报》2002年第3期27-29,共3页Journal of Natural Science of Heilongjiang University

摘　　要：[1]借助有限群的Sylow子群的正规性给出π-拟幂零群的概念,并利用子群的π-拟正规性得到π-拟幂零群的性质及几个充分条件,也探讨了π-拟幂零群与超可解群的关系。主要利用π-拟幂零群的极小子群及其它子群所具有的π’-拟正规性以及内超可解群的性质,假设π-拟幂零群不是超可解群,则它是内超可解群,从而得到矛盾。利用这种极小反例的方法给出超可解群的几个充分条件。Based on normality of Sylow subgroups of finite group, in [1] the author gave the definition of π-quasinilpotent group, and obtained the properties and some sufficient conditions with π -quasinormolity of its subgroups, and discussed the relationship between π - quasinilpotent group and supersolvable group. Using π-quasinonnality of minimal subgroups and other subgroups in addition to the properties of inner - supersolvable group, the authors suppose if π - quasinilpotent group isn't supersolvable, it is inner - supersolvable, which is contradictory. With this, some supersolvable group are obtained.

关 键 词：极小子群 超可解性 π-拟正规性 Π-拟幂零群 超可解群 内超可解群 极小反例 

分 类 号：O152.1[理学—数学]