Classification of All Primitive Groups of Degrees Four and Five

M. Mohammed Salih, Haval (2017) Classification of All Primitive Groups of Degrees Four and Five. Eurasian Journal of Science and Engineering, 3 (2). pp. 1-9. ISSN 24145629

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Abstract

Let be a compact Riemann surface of genus and be indecomposable meromorphic function of Riemann sphere by . Isomorphisms of such meromorphic functions are in one to one correspondence with conjugacy classes of tuples of permutations in such that and a subgroup of . Our goal of this work is to give a classification in the case where is of genus 1 and the subgroup is a primitive subgroup of or . We present the ramification types for genus 1 to complete such a classification. Furthermore, we show that the subgroups and of do not possesses primitive genus 1 systems.

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