超可解群的一些新判别准则Some criteria for supersolvability of finte groups
张丽
摘要(Abstract)：
结合有限群G的所有U-极大子群的交集Int_U(G),定义了U*-拟正规子群.有限群G的一个子群H称为U*-拟正规的,如果存在G的一个拟正规子群T,使得HT在G中是S-拟正规的,且(H∩T)H_G/H_G≤Φ(H/H_G)Int(G/H_G).利用U*-拟正规子群研究有限群的结构,得到了超可解群的一些新判别准则.
关键词(KeyWords)： 有限群;U*-极大子群;U*-拟正规子群;超可解群
基金项目(Foundation):
作者(Author): 张丽
DOI: 10.16393/j.cnki.37-1436/z.2016.05.002
参考文献(References)：
- [1]X.Chen,W.Guo,A.N.Skiba,On generalized-hypercentral subgroups of a finite group[J],J.Algebra,2015,442:190-201.
- [2]K.Doerk,T.Hawkes,Finite Soluble Groups[M],Walter de Gruyter,Berlin-New York,1992.
- [3]W.Guo,Structure Theory for Canonical Classes of Finite Groups[M],Springer,2015.
- [4]W.Guo,A.N.Skiba,On the intersection of themaximal subgroups and the generalized-hypercentre of a finite group[J],J.Algebra,2012,366:112-125.
- [5]B.Huppert,Endliche Gruppen I[M],Springer-Verlag,Berlin-New York,1967.
- [6]J.Huang,On s-quasinormal subgroups of finite groups[J],Comm.Algebra,2010,38:4063-4076.
- [7]A.N.Skiba,On the intersection of all maximalsubgroups of a finite group[J],J.Algebra,2011,343:173-182.
- [8]A.N.Skiba,On the-hypercentre and the intersection of all-maximal subgroups of a finite group[J],J.Pure Appl.Algebra,2012,216(4):789-799.
- [9]L.Zhang,W.Guo,L.Huo,On SΦ-embedded subgroups of finite groups[J].ТрудыИнститутаматематикиимеханикиУрОРАН,2016,22(1):310-318.