Niran Sabah Jasim et al Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 8( Version 3), August 2014, pp.01-08 www.ijera.com 1 | Page Tenser Product of Representation for the Group C n Suha Talib Abdul Rahman, Niran Sabah Jasim, Ahmed Issa Abdul Naby Department of Mathematics, College of Education for pure Science/Ibn-Al-Haitham, University of Baghdad Abstract The main objective of this paper is to compute the tenser product of representation for the group C n . Also algorithms designed and implemented in the construction of the main program designated for the determination of the tenser product of representation for the group C n including a flow-diagram of the main program. Some algorithms are followed by simple examples for illustration. Key Words: representation for the group, degree of the representation, character of representation, tenser product. Introduction The group of invertible nn matrices over a field F denoted by GL(n,F). The matrix representation of a group G is a homomorphism T:G  GL(n,F), the degree of this matrix is the degree of that representation [1], the trace for this matrix representation is the character of this representation, [2]. In this paper we consider the group C n = <x:x n = 1>. In section one the definition of tenser product introduced and apply that the f or representation of this groups by example, the main proposition introduce for the tenser product which we needed it in section two which include the algorithms designed and implemented in the construction of the main program designated for the determination of the tenser product of representation for the group C n . §.1 Preliminaries In this section, we recall definition proposition and remark which we needed in the next section. Definition 1.1 : [3] Let A  M n (ℂ), B  M m (ℂ), we defined a matrix A⊗B  M m (ℂ), put 11 12 1n 11 12 1n 11 12 1m 21 22 2n 21 22 2n 21 22 2m n1 n2 nn n1 n2 nn m1 m2 mm nm nm nn mm B B ... B ... β β ... β B B ... B ... β β ... β A B= ,A= ,B= B B ... B ... β β ... β                                                           Thus 11 12 1k 21 22 2k k1 k2 kk nm nm δ δ ... δ δ δ ... δ A B= δ δ ... δ               Where 11 11 11 12 11 1m 1n 11 1n 12 1n 1m 11 21 11 22 11 2m 1n 21 1n 22 1n 2m 11 1k 11 m1 11 m2 11 mm 1n m1 1n m2 1n mm mm mm β β ... β β β ... β β β ... β β β ... β δ = ,...,δ = ,... β β ... β β β ... β                                             RESEARCH ARTICLE OPEN ACCESS