ISSN: 1813-0410

Author : Abd Al-Moneem Said, Maany


On Artin Cokernel of the Group Dnh When n is an Odd Number

Maany Abd Al-Moneem Said; Hussein Hadi Abbas

journal of kerbala university, Volume 6, Issue 2, Pages 407-428

The group of all Z-valued characters of G over the group of induced unit characters from all cyclic subgroups of G forms a finite abelian group, called Artin Cokernal of G ,denoted by AC(G)= (G) /T(G)
The problem of finding the cyclic decomposition of Artin cokernel AC(Dnh) has been considered in this paper when n is an odd number , we find that if n = p .p ...p , where p1,p2,…, pm are distinct primes and not equal to 2 , then
AC(Dnh)= C2
= AC(Dn) C2
And we give the general form of Artin's characters table Ar(Dnh)when n is an odd number.