Existence of Smooth Epimorphism from Fuchsian Group to the Group of Automorphisms of compact Riemann surface to the point group of Carbon Tetrachloride

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Existence of Smooth Epimorphism from Fuchsian Group to the Group of Automorphisms of compact Riemann surface to the point group of Carbon Tetrachloride

Author & Affiliation:

MOLOYA BHUYAN

Department of Mathematics, DCB Girlsu2019 College, Jorhat-ASSAM (India)

CHANDRA CHUTIA

Department of Mathematics, Jorhat Institute of Science & Technology, Jorhat-ASSAM

Keyword:

smooth epimorphism, point group, compact Riemann surface, AMS Subject Classification 2020: 20B25, 20B30, 20H10, 30F10

Issue Date:

March 2020

Abstract:

A finite group G acts as a group of automorphisms on a compact Riemann surface S of genus g if and only if there exist a Fuchsian group $\Gamma$ and an epimorphism $\phi$ : $\Gamma$ $\rightarrow$ G such that ker $\phi$ = K is a surface group of genus g. And then $\phi$ is named as smooth homomorphism. The objective of this paper is to establish a set of necessary and sufficient conditions for the existence of smooth epimorphism from a Fuchsian group $\Gamma$ to the finite group of symmetries of Carbon Tetra chloride molecule, whose abstract group representation is $<$ a,b|a⁴= b³=(ab)² $>$ .

Pages:

13-21

ISSN:

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

Source:

Vol.32 - No.3

PDF:

Click here to download full paper

DOI:

http://dx.doi.org/10.22147/jusps-A/320301

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Copy the following to cite this article:

M. Bhuyan; C. Chutia, "Existence of Smooth Epimorphism from Fuchsian Group to the Group of Automorphisms of compact Riemann surface to the point group of Carbon Tetrachloride", Journal of Ultra Scientist of Physical Sciences, Volume 32, Issue 3, Page Number 13-21, 2020

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Available from: https://www.ultrascientist.org/paper/1526/

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