smarandache semigroups - w. kandasamy

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1、W.B.VasanthaKandasamySmarandacheSemigroupsx1→x1p1:x2→x3x→x32σ(1)=2µ(1)=3σ(2)=3µ(2)=1σ(3)=1µ(3)=2.o(G)po(G)−∑=o(Z(G)).N(a)≠Go(N(a))AmericanResearchPressRehoboth2002W.B.VasanthaKandasamyDepartmentofMathematicsIndianInstituteofTechnologyMadras,Chennai–600036,I

2、ndiaSmarandacheSemigroups10K0000K0101K0000K10A=MMKMM=In×n,MMKMM00K0001K0000K0110K00AmericanResearchPressRehoboth20021Thisbookcanbeorderedinapaperboundreprintfrom:BooksonDemandProQuestInformation&Learning(UniversityofMicr

3、ofilmInternational)300N.ZeebRoadP.O.Box1346,AnnArborMI48106-1346,USATel.:1-800-521-0600(CustomerService)http://wwwlib.umi.com/bod/andonlinefrom:PublishingOnline,Co.(Seattle,WashingtonState)at:http://PublishingOnline.comThisbookhasbeenpeerreviewedandrecommendedforpublica

4、tionby:Dr.MihalyBencze,Ro-2212Sacele,Str.Harmanului6.,Brasov,Romania.Dr.AndreiV.Kelarev,Prof.ofMathematics,Univ.ofTasmania,Australia.Dr.ZhangXiahong,Prof.ofMathematics,HanzhongTeachersCollege,China.Copyright2002byAmericanResearchPressandW.B.VasanthaKandasamyRehoboth,Box

5、141NM87322,USAManybookscanbedownloadedfrom:http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htmISBN:1-931233-59-4StandardAddressNumber:297-5092PrintedintheUnitedStatesofAmerica

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Preface51.Preliminarynotions1.1BinaryRelation71.2Mappings91.3Semigr

6、oupandSmarandacheSemigroups102.ElementaryPropertiesofGroups2.1DefinitionofaGroup132.2SomeExamplesofGroups132.3SomePreliminaryresults142.4Subgroups153.SomeClassicalTheoremsinGroupTheory3.1Lagrange'sTheorem213.2Cauchy'sTheorems223.3Cayley'sTheorem243.4Sylow'sTheorems254.S

7、marandacheSemigroups4.1DefinitionofSmarandacheSemigroups294.2ExamplesofSmarandacheSemigroups304.3SomePreliminaryTheorems334.4SmarandacheSubsemigroup354.5SmarandacheHyperSubsemigroup374.6SmarandacheLagrangeSemigroup394.7Smarandachep-SylowSubgroup414.8SmarandacheCauchyEle

8、mentinaSmarandacheSemigroup434.9SmarandacheCosets4435.TheoremforSmarandacheSemigroup5.1Lagrange'sTheoremforSma