The cyclic decomposition of cf (Q28×Cp)‎ R ̅(Q28×Cp)‎

Abstract EN

In this paper, we propose the cyclic decomposition of the factor group cf (Q28 × Cp), Z) / R ̅(Q28 × Cp), and the group cf (Q28 × Cp) is Z-valued class functions of the direct product group (Q28 × Cp) under the operation of addition, and R (Q28 × Cp) is the subgroup of the generalized characters of the group cf (Q28 × Cp, Z).

Then cf (Q28 × Cp) / (Q28 × Cp) is an abelian factor group denoted by K (Q28 × Cp) when Q28 the quaternion group |Q28| = 56, and |Cp| = p.

Also, we find the rational valued characters table of the group (Q28 × Cp) when p is prime numbers is given as following : ≡ * (Q28 × Cp) = ≡ * (Q28) ⨂ ≡ * (Cp) (1) and find the cyclic decomposition of group (Q28 × Cp) in this paper and prove that K (Q28 × Cp) = ⨁2 i=1 [K (Q28)] ⨁8 i=1 K (Cp) (2)