Title: The Cyclic Decomposition of the Group (Q2m C2) when m=2h , h ? Z+
Authors: Lecturer Rajaa Hassan Abass
Volume: 3
Issue: 7
Pages: 13-24
Publication Date: 2019/07/28//
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×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 any positive integer, then:
AC( Q2m×C2) =