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 cmaximal 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.
出处
《青岛大学学报（自然科学版）》
CAS
2005年第2期50-52,共3页
Journal of Qingdao University(Natural Science Edition)
关键词
极大子群
Θ-子群偶
幂零群
可解群
Maximal subgroup
theta pairs
nilpotent group
soluble group
