qp階亞循環(huán)群的弱q-DCI性.pdf

1、廣西大學(xué)碩士學(xué)位論文qp階亞循環(huán)群的弱qDCI性姓名：陳元芳申請學(xué)位級別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：徐尚進20050501廣西大學(xué)碩士學(xué)位論文印階亞循環(huán)群的弱q—DCI性THEWEAKqDCIPROPERTIESofMETACYCLICGROUPOFORDERqPABSTRACTThesymmetryofgraphshavealwaysbeenahotissueinstudyinggroupandgraphItismainlydesc

2、ribedbysometransitivitypossessedbytheautomorphismgroupsofthegraphsTheclassicalrepresentativesofsuchkindofgraphsareCayleygraphandSabidussicosetgraphWhenregardingtheisomorphismproblemoftheCayleygraph，itcanbedividedintotwoa

3、spects：thefirstaspectexploreswhentheCayleygraphswithinagroupareisomorphic；thesecondaspectexploresCayleygraphswithindifferentgroupscouldbeisomorphicRecentyears，mostpeoplearedoingresearchontheformerquestion，andmainlyfocuse

4、dontheCIpropertyofgraphIn1967，AdamsconjecturestartedtheresearchesoftheCIgroupandDCIgroupConcerningtheabeliangroupsandsolvablegroupstheresearchesonCIpropertieshadratherthoroughresultsuntilnowButfortheproblemoftheDCIproper

5、tyofmetacyclicgroups，therearestillnotmanyresultsIn1979，BabaiandFrankleposedaconjecturethatforanyoddprimenumberP，themetacyclicgroupoforder3pisaweak3CIgroupThisconjecturehasbeenrepudiatedbyShangjinXuandDianjunWangwithacoun

6、terexamplethatthemetacyclicgroupoforder21isnotaweak3DCIgroupQiongxiangHuanggavethesumcientandnecessaryconditionthataCayleysubsetisaweakDCIsubsetandprovedthattheDihedralgroupD2nisaweak2DCIgroupThepurposeofmythesisistoconi

7、tinuetheaboveworkonmetacyclicgroupsWefirstdiscussthemetacyclicgroupoforder5pitsgeneratingsubsetsindifferentclassesandthengivetheDCIpropertiesofthem，andprovethatrectacyclicgroupoforder55isnotaweak5DCISecondlyweextendthism

8、ethodofmetacyclicgroupoforder5ptothatoforderqP，andattainsimilarresultsThemethodusedinthisthesisismainlygrouptheoreticForconceptsofgrouptheoryandalgebraicgraphtheorywereferthereadersto[1，2，3]Keywords：Metacyclicgroup，Cayle