الخلاصة

The main purpose of this paper, is determination of the cyclic decomposition of the abelian factor group AC(G) = R (G)/T(G) where G = Q2m×C2 when m=2h , h Z+ (the group of all Z-valued characters of G over the group of induced unit characters from all cyclic subgroups of G). We have found that the cyclic, decomposition AC(Q2m×C2) depends on the elementary divisor of m as follows. if m = 2 h , h any positive integer, then: AC( Q2m×C2) = 2 2( 1) 1 C h i   