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THE CYCLIC DECOMPOSITION OF THE FACTOR GROUP CF(Dnh,Z)/R(Dnh) WHEN N IS AN ODD NUMBER | ||
| Journal of Kufa for Mathematics and Computer | ||
| Article 1, Volume 1, Issue 1, 2013, Pages 65-80 | ||
| Authors | ||
| Mohammed Shakir Mahdi; Hussein Hadi Abbas | ||
| Abstract | ||
| For fixed positive integer ,let Dn be the dihedral group, Dnh= Dn C2 and cf(Dnh,Z) be the abelian group of Z-valued class functions of the group Dnh .The intersection of cf(Dnh,Z) with the group of all generalized characters of Dnh , R(Dnh) is a normal subgroup of cf(Dnh,Z) denoted by (Dnh),then cf(Dnh,Z)/ (Dnh) is a finite abelian factor group which is denoted by K(Dnh). In this paper ,we determine the cyclic decomposition of the finite abelian factor group cf(Dnh,Z)/R(Dnh) when n is an odd number, we find that the cyclic decomposition of K(Dnh) depends on the elementary divisor of n ,if n= p .p ..p where p ,p ,…, p are distinct primes and , ,.., are positive integers, then ; K(Dnh)= K(Dn) C2 K(C4). And we find the rational valued characters table of the group Dnh. | ||
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