子群的正規(guī)指數(shù)、子群的s-正規(guī)性對有限群結(jié)構(gòu)的影響.pdf

1、蘇州大學(xué)碩士學(xué)位論文子群的正規(guī)指數(shù)、子群的s正規(guī)性對有限群結(jié)構(gòu)的影響姓名：殷霞申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：黎先華20060901TheInfluenceofnormalindexandsnormalityofSubgroupsAbstractTheInfluenceofNormalIndexandsnormalityofSubgroupsonTheStructureofFiniteGroupsAbstractLet日bea

2、propersubgroupofafinitegroupG，MisStnormalsubgroupofG，wecallIM／MO％ltobethenormalindexofHinG，ifMsatisfying(1)G=MH；(2)ifK司GandG=K日，thenlK／KnHaI≥IM／MA日舀1Wewrite礦(G：H)forthenormalindexofHinGAsubgroupHofafinitegroupGiscalledsn

3、ormalinG，ifthereexistsasubnormalsubgroupKofGsuchthatG=日ⅣandHnK≤lisa，whereHsGisthelargestsubnormalsubgroupofGwhichiscontainedinHThemainresultsofthispaperasfoliow：(1)WeobtainBorneresultsonsolvabilitypsolvabilityandpnilpote

4、ncyof缸itegroupsbythenumbertheorypropertyofnormalindexof2maximalsubgroupsandSylowsubgroups(2)WeobtainsomesufficientconditionsonsolvabilityoffinitegroupsbythesnormalityofSylownormalizersKeywords：normalindex，$normalitysolva