Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable

Thompson's theorem indicates that a finite group with a nilpotent maximal subgroup of odd order is solvable. As an important application of Thompson's theorem, a finite group is solvable if it has an abelian maximal subgroup. In this paper, we give some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable.http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000289364500008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701Mathematics, AppliedMathematicsSCI(E)中国科技核心期刊(ISTIC)中国科学引文数据库(CSCD)3ARTICLE5891-8962