Papers

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

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 (S₈) which is a finite point group of order 16 denote by D₁₆ generated by two elements having the presentation { u $\upsilon$ /u²= $\upsilon$ ⁸ = (u $\upsilon$ )² = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which D₁₆acts 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 $\mu$ ( $\geq$ 2) , $\mu$ $\geq$ | $\lambda$ |