Some Results On Association Scheme And Partitioned Group

In reference[4],B.Xu first constructs a new class of association schemes whose thin residues are thin?defined as?1.1??.It is prove.d that these constructions are indeed association schemes by the method of Schur rings.The properties of the automor-phism groups of these association schemes are obtained.Xu also gives a formula for the order of the automorphism group and a necessary and sufficient condition under which the associatoin scheme is Schurian.Several examples are provided at the end of this paper.In this thesis,we construct a non-schurian association scheme.Besides,the constructed association schemes satisfy conditions 1.1,where H is a partitioned group when K={1H}.In this thesis,we also get some results on partitioned group.Our main results are as follows:Remark:??G?is a partitioned number of G.· With hypothesis 1.1,let G = C₅ × C₅,H = E₄×C₃,and S be defined as in 1.1,then S is a non-schurian association scheme.· With hypothesis 1.1,let S be the association scheme on X defined 1.1,if Ni/N is a cyclic group.Moreover Comp_S?H,G?/Comp_s^N?H,G?is also a cyclic group,and|Comp_s?H,G?/Comp_s^N?H,G?||Ni/N|.· If G is a Frobenius group and the order of Frobenius kernel K of G has at least two prime diviors,then ??G?=|K|+1.· If G is a Partitioned group with every constituent being subnormal,then G is ap-group.· If G is an abelian group and G has a nontrivil partition,then G is an elemtary group.