The Cyclic Decomposition of cf(Q_28×C_p)/ R ̅(Q_28×C_p)

Abstract

In this paper, we propose the cyclic decomposition of the factor group cf(Q_28×C_p),Z)/R ̅(Q_28×C_p ), and the group cf(Q_28×C_p ) is Z-valued class functions of the direct product group (Q_28×C_p ) under the operation of addition, and R(Q_28×C_p )is the subgroup of the generalized characters of the group cf(Q_28×C_p,Z).Then cf(Q_28×C_p )/(Q_28×C_p ) is an abelian factor group denoted by K(Q_28×C_p ) when Q_28 the quaternion group |Q_28 |=56, and|C_p |=p. Also, we find the rational valued characters table of the group (Q_28×C_p ) when p is prime numbers is given as following: ≡^* (Q_28×C_p )=〖 ≡〗^* (Q_28 )⨂≡^* (C_p ) (1) and find the cyclic decomposition of group (Q_28×C_p ) in this paper and prove that K(Q_28×C_p )=⨁_(i=1)^2 [K(Q_28 )] ⨁_(i=1)^8 K (C_p ) (2)