COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OFΔ(3,3,k)  

作　　者：M.Ashiq Q.Mushtaq 

机构地区：[1]Department of Basic Sciences and Humanities College of E and ME National University of Sciences and Technology,Rawalpindi,Pakistan [2]Department of Mathematics Quaid-i-Azam University,Islamabad,Pakistan

出　　处：《Acta Mathematica Scientia》2008年第2期363-370,共8页数学物理学报（B辑英文版）

摘　　要：Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.

关 键 词：Coset diagrams conjugacy classes nondegenerate homomorphism projec tire line and triangle groups 

分 类 号：O152[理学—数学]