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1、OntheRiemannHypothesisinFunction-FieldsAuthor(s):AndreWeilSource:ProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica,Vol.27,No.7(Jul.15,1941),pp.345-347Publishedby:NationalAcademyofSciencesStableURL:http://www.jstor.org/stable/86919Accessed:
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6、STORtodigitize,preserveandextendaccesstoProceedingsoftheNationalAcademyofSciencesoftheUnitedStatesofAmerica.http://www.jstor.orgVOL.27,1941MATHEMATICS:A.WEIL345invariantsubgroupoforder1+3k.Sincesls2isoforder3wehave(S1s2)3=(SlS2-1S152)3=1.Itiseasytoprovethat
7、Sls2slgeneratesacyclicgroupwhosegeneratorsarecommutativewiththeirconjugatesundersiandunders2.Thatis,ifagroupcontainsamaximalsubgroupoforder3itcontainsaninvariantabeliansubgroupofindex3whichiseithercyclicoroftype1m.Thegroupswhichcontainmaximalsubgroupsoforde
8、r2oroforder3maythereforeberegardedasdetermined,butthosewhichcontainmaximalsubgroupsoforder2arenaturallyconsiderablysimplerthanthosewhichcontainmaximalsubgroupsoforder3.1Cf.thesePROCEEDINGS27,212-216(19
