c-27---正规子群和h-子群对有限群结构影响.pdf

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7、G

8、j~%(

9、G

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13、G

14、,21)=1.Gw,8~9A6Gc-

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16、G

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18、G

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21、G

22、j~Gjp-~9z"H(G),:Gp-

23、duatestudent:DengWenqiuSupervisor:ZhongXiangguiMajor:BasicMathematicsDirection:GroupTheoryGrade:2006AbstractIntheinvestigationoffinitegroups,usingsomepropertiesofsubgroupstocharacterizethestructureofgroupGcanobtainsomeprofoundresults.Thepurposeofthispaperistostudythe

24、influenceofc∗-normalsubgroupsandH-subgroupsonthestructureoffinitegroupssuchassolvability,p-supersolvability,p-nilpotency.Thepaperisdividedintotwochapters.Inthefirstchapter,weintroducetheinvestigativebackground,thepreliminarynotions,lemmasandthecorrelativeresults.Inthes

25、econdchapter,weusethepropertiesofthec∗-normalsubgroupsandH-subgroupstoinvestigatethestructureoffinitegroups,andobtainthefollowingresults:Theorem2.1.1LetGbeafinitegroupandNbeanormalsubgroupofGsuchthatG/Nisp-nilpotent,wherepisaprimedivisorof

26、G

27、.IfeveryminimalsubgroupAof

28、anySylowp-subgroupofNisc∗-normalinGandN(A)isp-nilpotent,thenGisp-nilpotent.GTheorem2.1.4LetGbeafinitegroupandpbeaprimedivisorof

29、G

30、,(

31、G

32、,p2−