Complete Classification of Degree 7 for Genus 1

Peshawa M Khudhur

doi:10.24996/ijs.2021.62.2.25

Abstract

Assume that is a meromorphic fuction of degree n where X is compact Riemann surface of genus g. The meromorphic function gives a branched cover of the compact Riemann surface X. Classes of such covers are in one to one correspondence with conjugacy classes of r-tuples ( of permutations in the symmetric group , in which and s generate a transitive subgroup G of This work is a contribution to the classification of all primitive groups of degree 7, where X is of genus one.

Highlights

A function is a non-constant meromorphic function from compact connectedRiemann surface X of genus g to Riemann sphere, if it can locally be described as two holomorphic functions
The mesomorphic function is of degree if the order of the fiber (| ( ) for general equal to
We introduce the Nielsen classes as follows

Summary

Introduction

A function is a non-constant meromorphic function from compact connectedRiemann surface X of genus g to Riemann sphere , if it can locally be described as two holomorphic functions. Lemma 3.3: Let G be a group and , where acts on the right cosets of maximal subgroup of the group .

Results

Conclusion