用置換群理論構造具有特殊傳遞性的組合結構（Ω，Λ，Ι）.pdf

1、◆鞲淅江大學博士學位論文ABSTRAaTThispaperaimsatdiscussingtheautomorphJsmgroupsofcombinatorialstruetnres(Q，A，z)，whichareexplainedas2(o，凳，1)designsorgraphsrespectivelywhencomestoconcretediscussions’InChapter1，wegiveacomprehensivesurve

2、yofthebackgroundsandmodemdevelopmentsoftheautomorphismgroupsofcombinatorialstructures(n，A，刁，inwhichweemphasizetheapplicationsofthenewtheoriesandnewtoolsdevelopedinabstractgroupsandpermutationgroupstotheclassificationof(Q

3、，A，Z)tInChapter2，weexplain(n，A，z)as2(u，k，1)designsanddeterminethedesignsadmittingablock—primitiveautomorphismgroupisomorphictoPSU(3，qo)Partoftheworkinthischapteristohsta噩subgroupsofPSU(3，q2)，whichisakeysteptodeterminethe

4、correspondingdemgnsThemethodsweusec823begen，eralizedandthenappliedtodeterminethestructuresofanarbitraryclassicalgroupC(n，K))vhennisnotlargeAnotherworkistoprovethatany2(u，k，1)designadmittingapointtransitiveautomorphismgro

5、upisomorphictoPSU(3：q2)isnotaprojectiveplanetherestfltscanbegeneralizedtodeterminewhetheranalmostsimplegroupcanactasapoint—transitivecollineationgroupofaprojectiveplaneornotThemainresultsinChapter2arethefollowing：MainThe

6、orem1LetobeaprojectiveplaneandGacoUineationgroupofoI|GistransitiveonthepointsofD，thenGisnotisomorphictoPSU(3、q2)MainTheorem2Let口bea2(v，≈，1)designandG然automorphismgroupoiD盯GisprimitiveontheblocksandG魯PSU(3，礦)，then口isaHerm

7、itianUnitalInChapter3，weexplain(n，A，司asgraphsanddiscusstheclassificationof2aretransitivegraphsadmittinganautomorphismgroupisomorphictothesporadicsimplegroup五Themainresu／tsinChapter3arethefollowing：Theorem1LetG=JxSupposet

8、hatF=(G，ZTgT)isa(G，2)一aretrar捕itivegraphthenuptoanisomorphism，T，gandFatedetermined(Theyarelistednthetableonpage2jTheorem2LetFbeoneofthegraphsinTheoremijGtsprimitiveonthepoints對FthenAutF=G：I|GisimprimitiveonthepointsofFan