关于有限群的广义Frattini子群  

On Generalized Frattini Subgroup of a Finte Group

作　　者：王玉雷[1] 王志俊[1] 

机构地区：[1]青岛大学数学系,山东青岛266071

出　　处：《青岛大学学报（自然科学版）》2005年第2期50-52,共3页Journal of Qingdao University(Natural Science Edition)

摘　　要：定义了一类极大子群的交Φπ(G),它是Frattini子群的推广,利用它和极大θ-子群偶的性质,给出了幂零群和可解群的几个充要条件.in[3]and[4],the authors give some necessary and sufficient conditions for a soluble group by using the properties of cmaximal subgroup and theta pairs for a maximal subgroup.in this article, Φ_π(G) is defined to be the intersection of a class of the maximal subgroups of G ,which is a generalization of the Frattini subgroup of G. Some necessary and sufficient conditions for a nilpotent group and a soluble group are also obtained in virtue of the properties of the generalized Frattini subgroup and theta pairs for a maximal subgroup.

关 键 词：极大子群 Θ-子群偶 幂零群 可解群 

分 类 号：O152.1[理学—数学]