有限幾乎單群的OD-刻畫(huà)與非交換圖刻畫(huà).pdf

1、蘇州大學(xué)博士學(xué)位論文有限幾乎單群的OD刻畫(huà)與非交換圖刻畫(huà)姓名：張良才申請(qǐng)學(xué)位級(jí)別：博士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：施武杰20080301有限幾乎單群的OD刻畫(huà)與非交換圖刻畫(huà)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