2-（v,k,l）設(shè)計(jì)的區(qū)傳遞自同構(gòu)群.pdf

1、浙江大學(xué)博士學(xué)位論文2（vkl）設(shè)計(jì)的區(qū)傳遞自同構(gòu)群姓名：韓廣國(guó)申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：基礎(chǔ)數(shù)學(xué)代數(shù)學(xué)指導(dǎo)教師：李慧陵20030101ABSTRACTThisthesisisdevotedtoclassifyingblockdesignswhoseautomorphismgroupGactstransitivelyOUblocksItconsistsoffourchaptersInChapter1，weintroducethebackg

2、roundofgroupsanddesignsandsummarythemainresultsInChapter2，weintroducesomebasiccontentsofgroupsandblockdesignsTheclassificationofblock—transitive2一和，3，1)designswascompletedmorethantwentyyearsagoIn【10】CaminaandSiemonsclass

3、ified2一(“，4，1)designswithablock—transitive，solvablegroupsofautomorphismsLiclassified2一(∞，4，1)designsadmittingablocktransitive，unsolvableautomorphismgroups(see【49])In【50】LiandTongclassified2～(口：5，1)designswith8blocktransi

4、tive，solvablegroupsofautomorphismsSoforblocktransitive2一扣，5，1)designs，weneedtostudythecaseinwhichthegivenblocktransitivegroupofautomorphismsisunsolvableInChapter3weconsiderthiscaseandprovethefollowingtheoremTheorem31Ifab

5、locktransitivegroupofautomorphismsofa2一(“，5，1)designisunsolvable，thenitisflag—transitive，ByTheorem31andtheresultofLiandTong[50]，theclassificationofblock—transitive2一p，5，1)designswascompleted。AndwehaveCorollary32Let口bea2一

6、(“，^，1)design，G≤Aut(T))beblocktransitivebutnotflagtransitive，thenGissolvableandoneofthefollowingistrue(1)ifGispointimprimitive，thenV=21，andG≤歷1：Zs；(2)ifGispointprimitivethenG≤ArL(1，口)and∞=礦，wherePisaprimenumberwithP三21(r

7、ood40)，andaanoddinteger，InChapter4，weconsider2一㈠≈，1)(女=6，7，8，9)designswithablocktransitive，unsolvablegroupsofautomorphisms。WegetthefollowingresultTheorem41Let口bea2一扣，k，1)(≈=6，7，8，9)designwithG冬Aut(9)blocktransitive，point

8、—primitivebutnotflagtransitiveIfGisunsolvable，thenwehave(1)ifk=6and(女，u)≠2，thenthesocleofGisnottheexceptionalsimplegroupsofLietype(2)if≈=7，thenthesocleofGisnottheexceptionalsimplegroupsofLietype(3)if≈=8，thenthesocleofGis