الخلاصة

Abstract The main purpose of this paper, is determination of the cyclic decomposition of the abelian factor group AC(G) = (G)/T(G) where G = Q2m×Cp when m=2h , h ∈ Z+ and p is prime number (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×Cp) depends on the elementary divisor of m as follows. if m = 2 , h any positive integer and p is prime number, then: AC( Q2m×Cp) = We have also found the general form of Artin's characters table of Ar(Q2m×Cp) when m=2h , h ∈ Z+ and p is prime number.