On Artin Cokernel of The Quaternion Group Q2m When m=2h ,h any positive integers Number
Abstract
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 .
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Published
04.10.2024