Title: The group's table of Rational valued characters (Q2m×C9) When m=2h, h? Z+
Authors: Huda Qusay Hashim
Volume: 10
Issue: 3
Pages: 162-170
Publication Date: 2026/03/28
Abstract:
This topic examines the table of characters with rational values for the group (Q2m× C9). Q2m represents the generalized Quaternion group of order 2m, while C9 represents the cyclic group of order 9. The symbol (×) denotes the direct product between the two groups. In this case, m = 2h, where h is a positive integer and m is an even number. This topic focuses on finding the irreducible table of characters for the set resulting from the direct product and studying characters whose values are exclusively rational. This is achieved by relying on the properties of the direct product of groups. The characters of the set (Q2m× C9) can be obtained by multiplying the characters of both groups (Q2m and C9). Analyzing these characters helps in understanding the structure of the group and its representations, which is an important topic in the theory of finite set representations.