Classification of All Primitive Groups of Degrees Four and Five

Author : Haval M. Mohammed Salih

Abstract:   Let be a compact Riemann surface of genus g and µ:X→𝕡1 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(x, x,…xr) of permutations in Sn such that x1, x2,…xr=1 and G=< x1, x2,…xr> a subgroup of Sn. 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  Cof 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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Eurasian Journal of Science & Engineering
ISSN 2414-5629 (Print), ISSN 2414-5602 (Online)