The mathematics of Donald Gordon Higman.pdf

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1、ThemathematicsofDonaldGordonHigmanversion14December,2008EiichiBannaiDepartmentofMathematicsKyushuUniversityFukuoka,Japanbannai@math.kyushu-u.ac.jpRobertL.Griess,Jr.DepartmentofMathematicsUniversityofMichiganAnnArbor,MI48109USArlg@umich.eduCherylE.Prae

2、gerSchoolofMathematicsandStatistics(M019)UniversityofWesternAustralia35StirlingHighwayCrawleyWA6009,Australiapraeger@maths.uwa.edu.auLeonardScottDepartmentofMathematicsUniversityofVirginiaarXiv:0901.0971v1[math.HO]8Jan2009Charlottesville,VirginiaUSAll

3、s2l@virginia.edu1Contents1Introduction31.1Acknowledgements........................42AbriefoverviewofDonaldHigman’simpactonmathemat-ics.53Education,influencesandemployment74Detailsofearlywork:grouptheoryandrepresentationthe-ory74.1Focalsubgrouptheorem..

4、...................84.2Representationtheory......................94.3InfluenceoftheworkofDonaldHigman,byCharlesCurtis..105Detailsoflaterwork:algebraiccombinatorics,groupsandgeometries115.1ABAgroups,rank2geometrycharacterization.........115.2Rank3permut

5、ationgroups...................115.3TheHigman–SimsgraphandtheHigman–Simssporadicsim-plegroupoforder44,352,000=2932537·11...........125.3.1MesnerthesisandHigmanSimsgraph.........145.4Stronglyregulargraphsandassociationschemes........155.5CoherentConfigur

6、ations.....................155.6Geometricapplicationsofcoherentconfigurations.......175.7Connectionswithstatistics,topology,mathematicalphysics..196YoungermathematiciansandDonaldHigman196.1MichaelAschbacher........................196.2R.A.Bailey.......

7、.....................206.3EiichiBannai...........................216.4PeterJ.Cameron.........................256.5RobertL.Griess,Jr........................256.6WillemHaemers..........................276.7CherylE.Praeger.........................276.8C.

8、C.Sims.............................286.9StephenD.Smith.........................286.10JohnG.Thompson........................2826.10.1AbouttheTheOddOrderTheorem..........296.11Studentsandassociates......................296.11.1ListofDoctoralStud