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	ON A THEOREM OF HUPPERT
	Shi, Jiangtao ; Zhang, Cui
	2011
关键词	Finite group soluble group supersoluble group
英文摘要	A well-known theorem of Huppert states that a finite group is soluble if its every proper subgroup is supersoluble. In this paper, we proved the following result: let G be a finite group. (1) If G has exactly n non-supersoluble proper subgroups, where 0 <= n <= 7 and n not equal 5, then G is soluble. (2) G is a non-soluble group with exactly five non-supersoluble proper subgroups if and only if all non-supersoluble proper subgroups are conjugate maximal subgroups and G/Phi(G) congruent to A(5), where Phi(G) is the Frattini subgroup of G. Furthermore, we also considered the influence of the number of non-abelian proper subgroups on the solubility of finite groups.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000290495300009&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Applied; Mathematics; SCI(E); 0; ARTICLE; 2; 295-301; 10
语种	英语
出处	SCI
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314444]
专题	数学科学学院
推荐引用方式 GB/T 7714	Shi, Jiangtao,Zhang, Cui. ON A THEOREM OF HUPPERT. 2011-01-01.

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