 محمد شاكر زبيبه ( مدرس ) كلية التربية للبنات - الرياضيات [email protected] 07809448081  THE CYCLIC DECOMPOSITION OF THE FACTOR GROUP CF(Dnh,Z)/R(Dnh) WHEN N IS ANODD NUMBER تحميل بحث النوع: علوم التخصص العام: Husein Hadi Abbass اسم الناشر: Mohammed Shakir Mahdi اسماء المساعدين: Journal of Kufa for Mathematics and Computer الجهة الناشرة: Iraq 2010 سنة النشر: الخلاصة For fixed positive integer n³3 ,let Dn be the dihedral group, Dnh= Dn ÏC2 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 R (Dnh),then cf(Dnh,Z)/ R (Dnh) is a finite abelian factor group which is denoted by K(Dnh). I n 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 ofn ,if n= p 11a.p 22 a..p mmawhere p1 ,p 2 ,…, p m are distinct primes and 1 a , 2 a ,.., m a are positive integers, then ; K(Dnh)= 2 1 = Å i K(Dn) ( )( ) ( )2 1 1 1 1 1+ × 2 + + - = Å m i a a L a C2 Å K(C4). And we find the rational valued characters table of the group Dnh.