On The Factor GroupK(Dn×C3When n =2h)

Abstract

Let Dn be the dihedral group and C3 be the cyclic group of order 3 . Let cf(Dn×C3,Z) be the abelian group of Z-valued class function of the group Dn×C3. The intersection of cf(Dn ×C3,Z) with the group of generalized characters of Dn ×C3 which is denoted by R( Dn×C3 ) is a normal subgroup of the group cf(Dn ×C3,Z)denoted by (Dn×C3) . The factor group cf(Dn ×C3,Z)/ (Dn×C3) is afinite abelian group denoted by K(Dn×C3) .In this paper, we prove that the rational valued characters table of the group D ×C3 is equal to the tensor product of the rational valued characters table of D and the rational valued characters table of the cyclic group C3 . Also, we find that K(D ×C3)= .