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Category: Issue 7

Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule

RAFIQUL ISLAM
Department of Mathematics, Jorhat Engineering College, Jorhat-785007 (India)
CHANDRA CHUTIA
Department of Mathematics, Jorhat Institute of Science and Technology, Jorhat (India)

ABSTRACT:

In this paper, we consider the group of symmetries of the Sulphur molecule (S) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation { u\upsilon/u2\upsilon8 = (u\upsilon)2 = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which  D16 acts as a group of automorphisms as follows:

D16 the group of symmetries of the sulfur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers \lambda and \mu such that \lambda \leq 1 and \mu \geq 1 and
g=\lambda +8\mu (\geq2) , \mu\geq |\lambda|

KEYWORDS: Symmetries, Fuchsian group, Smooth quotient, Riemann surface,