On the Rational Valued Character of the Group Dn×C3 when n is an Odd Number

Abstract

Let D_n be the dihedral group , C₂ be the cyclic group of order 2 and D_nh is the direct product group of D_n and C₃ (i.e. D_n×C₃) . Let  cf(D_n ×C₃,Z) be the abelian group of Z-valued class functions of the group D_n ×C₃ . The intersection cf(D_n ×C₃,Z) with the group of all generalized characters of D_n ×C₃ which is denoted by (D_n ×C₃) , is a normal subgroup of cf(D_n ×C₃,Z) denoted by

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