On Artin Cokernel of The Group Dnh When n is an Even Number

For a finite group G ,let R(G) denotes the group generated by Z-valued characters of G under the operation of pointwise addition ,inside this group there is a subgroup generated by Artin's characters , which will be denoted by T(G) .Awell known theorem due to Artin asserted that T(G)has a finite index in R(G).The factor group R(G) /T(G) is called Artin cokernel of G which is denoted by AC(G) ,and it is a finite abelian group of exponent A(G). The problem of determining the cyclic decomposition of AC(G) seems to be untouched. In this work ,G is considered to be Dnh=DnxC2 and the reason for such consideration is the close relation between AC(G) and the factor group cf(G,Z)/R(G) ,where cf(G,Z) is the group of all z-vauled class functions on the group G .