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

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

Author & Affiliation:

RAFIQUL ISLAM

Department of Mathematics, Jorhat Engineering College, Jorhat-785007 (India)

CHANDRA CHUTIA

Department of Mathematics, Jorhat Institute of Science and Technology, Jorhat (India)

Keyword:

Symmetries, Fuchsian group, Smooth quotient, Riemann surface,

Issue Date:

July 2020

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) , $\mu$ $\geq$ | $\lambda$ |

Pages:

88-92

ISSN:

2319-8044 (Online) - 2231-346X (Print)

Source:

Vol.32 - No.7

PDF:

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DOI:

http://dx.doi.org/10.22147/jusps-A/320701

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Copy the following to cite this article:

R. Islam; C. Chutia, "Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule", Journal of Ultra Scientist of Physical Sciences, Volume 32, Issue 7, Page Number 88-92, 2020

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Available from: https://www.ultrascientist.org/paper/1535/

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License