The cyclic decomposition of cf (Q2q×C10)‎ R ̅ (Q29×C10)‎

Abstract EN

In this paper, we propose the cyclic decomposition of the factor group cf (Q2q × C10)‚ Z) / R ̅(Q2q × C10), and the group cf (Q2q × C10‚Z) is Z-valued class functions of the direct product group ((Q14 × C10)) under the operation of addition, and R ((Q14 × C10)) is the subgroup of the generalized characters of the group cf (Q2q × C10)‚ Z).Then cf (Q2q × C10‚ Z) / R ̅(Q2q × C10)) is an abelian factor group denoted by K (Q2q × C10) where (Q14 is the quaternion group of order 28 and C10 is the cyclic group of order 10.

Also, we find the rational valued characters table of the group (Q2q × C10) when p, and q prime numbers and s ∈ Z+ is given as follows : ≡ * (Q2q × C10)) = ≡ * ((Q14) ⨂ ≡ * (C10) (1) and find the cyclic decomposition of group (Q2q × C10) in this paper and prove that K (Q2q × C10) = ⨁ 4 i=1 [KQ2q] ⨁ 5 i=1 K (C10) (2)