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

AUTHOR AND
AFFILIATION

MOLOYA BHUYAN
Department of Mathematics, DCB Girlsu2019 College, Jorhat-ASSAM (India)
CHANDRA CHUTIA
Department of Mathematics, Jorhat Institute of Science & Technology, Jorhat-ASSAM

KEYWORDS:

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

Issue Date:

March 2020

Pages:

13-21

ISSN:

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

Source:

Vol.32 – No.3

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DOI:

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

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\rightarrowG 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 >.

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


Copy the following to cite this URL:

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

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