The Cyclic decomposition and the Artin characters table of the group (Q2m Cp) when m=2h , h ∈ Z+ and p is prime number

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 = Q_2m×C_p when m=2^h , 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(Q_2m×C_p) depends on the elementary divisor of m as follows.

if  m = 2 , h any positive integer and p is prime number, then:

AC( Q_2m×C_p) =

We have also found the general form of Artin's characters table of Ar(Q_2m×C_p) when m=2^h , h  Z⁺ and p is prime

 number.