有限幾乎單群的OD-刻畫與非交換圖刻畫.pdf

1、蘇州大學博士學位論文有限幾乎單群的OD刻畫與非交換圖刻畫姓名：張良才申請學位級別：博士專業(yè)：基礎(chǔ)數(shù)學指導教師：施武杰20080301有限幾乎單群的OD刻畫與非交換圖刻畫AbstractDDcharacterizationandNon—commutingGraphCharacterizationofFiniteAlmostSimpleGroupsAbstractItiswellknownthatfinite(almost)simplegr

2、oupsarebricksoffinitegroupsInordertoknowbettertheirpropertiesandstructures，itisveryhelpfulfortlStocharacterizethembytheirobvious，simpleandinstinctivepropertiesThispaperisintendedtostudythefollowingpropertiesoffinitealmos

3、tsimplegroups：thedegreesofverticesoftheirprimegraphsandtheirnoncommunicatinggraphsObviouslythereis眥intimaterelationbetweentheformerproblemandaconjectureputforwardbyProfessorWujieShiin1987(see【531)Thelatteroneisrelatedtoa

4、notherconjecturenamedAAM’SconjectureputforwardinJAlgebrain2006(see【1])BothoftheseconjecturesarestillunsolvedcompletelyInChapter1，weintroducesomesymbolsandbasicconceptsthatweusuallyuseinthepaperMoreover，weintroducesomebac

5、kgroundsandresultsofOUrresearchInChapter2，westudyODcharacterizationofsomefinitealmostsimplegroupsNamelyweclassifysomefinitealmostsimplegroupswhichhavesaIneordersanddegreesofverticesoftheirprimegraphsSomeresults，partlyorc

6、ompletelygeneralizepreviousresultstechnologicallyorextensivelyInChapter3，westudycharacterizationofsomefinitealmostsimplegroups，speciallythosewithconnectedprimegraphs，bytheirnoncommunicationgraphsNotonlyhavewesetupalinkbe

7、tweenAAM’SconjectureandThompson’8conjectureforthefinitesimplegroupswithnonconnectedprimegraphs，butalsowehavefoundaseriesofexamplestoshowthattheformerconjectureisalsotrueforthefinitesimplegroupswithconnectedprimegraphsAtt