On Artin Cokernel of The Quaternion Group Q2m When m=2h ,h any positive integers Number

الملخص

In this article we find the cyclic decomposition of the finite abelian factor group AC(G)=

R

(G)/T(G) where G = Q2m and

2

h

m  ,

h any positive integers and Q2m is the Quaternion group of order 4m.

(the group of all Z-valued generalized characters of G over the group of induced unit characters from all cyclic subgroups of G) .

 We find that the cyclic decomposition AC(Q2m) depends on the elementary divisor of m

If

2

h

m  , h any positive integers , then :

AC(Q2m)=

1

1

h

i







C2

Moreover, we have also found the general form of Artin characters table Ar(Q2m) when m is an even number .