摘要
证明了下述定理：定理１（ｋｒａｒｎｅｒ定理的推广）设Ｇ为有限可解群，Ｇ／Ｎ为超可解群．如果对某ｋ及Ｇ的每一极大子群Ｌ均有等于１或素数，则Ｇ为超可解群，其中Ｆ＿ｎ（Ｇ）归纳定义如次：定理２设群Ｇ有限可解，为满整群系｛ｆ（ｐ）｝所局部定义的群系。
heoren 1 Assume that G is a finite solvable group and G/N is supersolvable.or a prime for some k and each maximal subagoup L of G,then G is supersolvable,whereF_n(G) are defind by induction as following Theorem 2 Assume that G is a finite solvable group,is a formation locally defined by a set of full and integrated formations.If G/N and there exists chief series from Φ(N)toFit(N)of G such that
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
1994年第1期1-4,共4页
Journal of Southwest China Normal University(Natural Science Edition)
关键词
克雷默定理
超可解群
费廷子群
Kramer' s theorem
supersolvable groups
Fitting subgroups
loeally defined formations
