12709.弱h子群與弱h子群對有限群結(jié)構(gòu)的影響

1、弱H一子群與弱日術(shù)一子群對有限群結(jié)構(gòu)的影響專業(yè)名稱：基礎(chǔ)數(shù)學(xué)申請人：鄭飛指導(dǎo)教師：盧家寬論文答辯委員會委員：么羝：委員：么塑墜：知迭狄；廣西師范大學(xué)碩士學(xué)位論文弱H一子群與弱日‘一子群對有限群結(jié)構(gòu)的蘭!：————————————————————————————————————————————————————一TheInfluenceofWeaklyH一日木一S_trucStuubregrounpsnaitnedWeaklySubgrou

2、psontheofGroupsGraduatestudent：ZhengFeiSupervisor：AssociateProfessor：LuJiakuanMajor：FundamentalMathematicsSpeciality：GroupTheoryGrade：2013ABSTRACTLetGbeafinitegroup，H≤GHiscalledanH—subgroupofGifNa(H)nH9≤Hforallg∈G：Hiscal

3、ledaweaklyH—subgroupinGifthereisanormalsubgroupKofGsuchthatG：HKandHnKisanH—subgroupinG；HiscalledaweaklyH’一subgroupinGifthereisasubgroupKofGsuchthatG=HKandHnKisanH—subgroupinGInthestudyoffinitegroups，usingsomeofthepropert

4、iesofspecialsubgroupstocharacterizethestructureoffinitegroupsisanimportantmethodInthispaper，byusingthepropertiesofweaklyH—subgroupandweaklyH‘一subgroupofprimepowerorder，weinvestigatethecharacterizationofnilpotent，supersol

5、vabilityandpnilpotentofG，andwegetsomenewcharacterizationsofnilpotent，supersolvabihtyandpnilpotentofGThispaperisdividedintotwochaptersnThefirstchapter，wemainlygivetheconceptofweaklyH—subgroupandweaklyH’subgroup，introducet

6、heinvestigativebackground，thepreliminarynotionsandsomerelevantknownresultsthemainpropertiesandrelevant1emmaswhicharerelatedtoweaklyH—subgroupandweaklyH‘subgroupInthesecondchapter，byusingtheweaklyH—subgroupandweaklyH一subg

7、roupofprimepowerorderofG，wegetsomesufficientconditionsforafinitegroupGtobenilpotent，pnilpotentandsupersolvableWeobtainsomemainresultsasfollows：Theorem211LetGbeafinitesubgroupsoforderPandorder4(P=2)groupandPtheprimediviso

8、rofGIIfallcyclicofGarein形(G)，thenGispnilpotentTheorem212LetGbeafinitegroupandPtheprimedivisoroflGI，NbeanormalsubgroupofGsuchthatG／NispnilpotentIfeverysubgroupoforderPofNiscontainedin瓦(G)，andeverycyclicsubgroupsoforder4wh

9、enP=2ofNarein形(G)，thenGispnilpotentTheorem213LetGbeafinitegroup，NbeanormalsubgroupofGsuchthata／NispnilpotentIfeverysubgroupoforder4ofF(Ⅳ)isweakly日一subgroupinGThenGisnilpotentifandonlyifeverysubgroupoforderPofF’(Ⅳ)isconta