When n is an odd number

Abstract EN

The group of all Z-valuedgeneralized characters of G over the group of induced unit characters from all cyclic subgroups of G, AC(G)= R (G)/T(G) forms a finite abelian group, called ArtinCokernel of G .The problem of finding the cyclic decomposition of Artincokernel AC( ) has been considered in this paper when n is an odd number , we find that if n = p 1 1  .p 2 2  ..p m m  , where p1,p2,…, pm are distinct primes and not equal to 2 , then : AC( )= 2( 1 1 1 ) 1  1 2      1 m i           C2 = 2 i 1  AC(Dn)  C2 And we give the general form of Artin's characters table Ar( )when n is an odd number .