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 and an epimorphism
:
G such that ker
= K is a surface group of genus g. And then
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
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, 2020Copy 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, 2020Available from: https://www.ultrascientist.org/paper/1526/