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1、22F4(q)isalso7′2groupbylemma1,therefore,F4(q)cannotbeinner72closedgroup,and(2.8)holds.22m+12(2.9)GisnotoftypeG2(q),q=3,mE1,Dn(q),n>3.2LetX=G2(q),S∈Syl2(X),by[12,p.292],onehasCX(S)=S,ûNX(S)û=168,22itfollowsthatNX(S)isnot72closedgroupandG2(q)cannotbeinner72cl
2、osedgroup.ForDn2(q),withthesameargumentbefore,weneedtoconsideronlyD4(q).ItisknownthatA2(q)222andA1(q)3D3(q)areLevisubgroupsofD4(q).Forasameq,bothA2(q)andD3(q)arenot27′2groupatthesametimebylemma1,henceD4(q)cannotbe72closedgroup,and(2.9)holds.TheproofoftheThe
3、oremiscompletebytheclassificationtheoremoffinitegroups.References[1]ChenZhongmu,Ontheinnerp2closedgroups,AdvancesinMath.,15(1986),385-388.[2]LiShirongandLiShiyu,Finitegroupsinwhicheverynon2maximalpropersubgroupis32closed,ActaMath.Sinica.,29(1986),498-503.[3
4、]YouTaijie,Onthestructureofinner52closedsimplegroups,[4]XiaoWenjun,Onp2closedgroups,ActaMath.Sinica,36(1993),160-162.[5]M.Bloom,ThesubgroupsofPSL(3,q)foroddq,Trans.Amer.Math.Soc.,127(1967),150-178.[6]B.Huppert,EndlicheGruppenI,Springer2Verlag,BerlinHeidelbe
5、rg,NewYork,1979.[7]J.H.Conway,R.T.Curtis,S.P.Norten,R.A.ParkenandR.A.Wilson,AtalsofFiniteGroups,ClarendonPress,Oxford,1985.[8]R.W.Carter,SimpleGroupsofLieType,Wiley,Londom,1972.[9]B.Kleidman,ThemaximalsubgroupsoftheChevalleygroupsG2(q)withqoddtheReegroups2G
6、2(q),andtheirautomorphismgroups,Jour.ofAlg.,117(1988),30-71.[10]D.Gorenstien,FiniteGroups,Harper&Row,NewYork,1968.[11]L.E.Dickson,Lineargroups,withanexpositionoftheGaloisfieldtheory,Teubner,Leipzig,1901.[12]B.Huppert,FiniteGroupsIII,Springer2Verlag,BerlinHe
7、idelberg,NewYork,1982.关于内72闭单群的结构李先崇游太杰(贵州师范大学数学系,贵阳550001)摘要研究内p2闭群的结构是一个很活跃的课题.对于p=2,3,5的内p2闭群的结构已经被确定(见[1,2,3]).本文确定内72闭单群的结构.—175—©1995-2005TsinghuaTongfangOpticalDiscCo.,Ltd.Allrightsreserved.JournalofMathematicalResearch&ExpositionVol.17,No.2,171-175,
8、May1997XOntheStructureofInner7-ClosedSimpleGroupsLiXianchongYouTaijie(Dept.ofMath.,GuizhouNormalUniversity,Guiyang550001)AbstractThestructureofinnerp2closedgroupsforp=2,3,5areknown(see[1,2,3]).Inthispa
