Author : Haval M. Mohammed Salih ^1&2
1Soran University, Faculty of Science, Mathematics Department, Soran, Iraq
²Ishik University, Faculty of Education, Mathematics Department, Erbil, Iraq

Abstract:   Let be a compact Riemann surface of genus g and µ:X→?¹ be indecomposable meromorphic function of Riemann sphere by . Isomorphisms of such meromorphic functions are in one to one correspondence with conjugacy classes of r tuples(x₁ , x₂ ,…x_r) of permutations in S_n such that x₁, x₂,…x_r=1 and G=< x₁, x₂,…x_r> a subgroup of S_n. Our goal of this work is to give a classification in the case where X is of genus 1 and the subgroup G is a primitive subgroup of S₄ or S₅ . We present the ramification types for genus 1 to complete such a classification. Furthermore, we show that the subgroups D₁₀ and  C₅ of S₅ do not possesses primitive genus 1 systems.

Keywords:   Primitive Groups, Indecomposable Meromorphic Functions, Genus Systems

doi: 10.23918/eajse.v3i2p1

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