Classification of All Primitive Groups of Degrees Four and Five
DOI:
https://doi.org/10.23918/eajse.v3i2p1Keywords:
Primitive Groups, Indecomposable Meromorphic Functions, Genus SystemsAbstract
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 ,…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 C5 of S5 do not possesses primitive genus 1 systems.
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