Journal of Ultra Scientist of Physical Sciences - A
Voulume: 32
Issue: 7
Article No. 1
Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule
Department of Mathematics, Jorhat Engineering College, Jorhat-785007 (India)
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 (S8 ) 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 sulphur (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|

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