Journal of Ultra Scientist of Physical Sciences - A
Voulume: 32
Issue: 3
Article No. 1
Existence of Smooth Epimorphism from Fuchsian Group to the Group of Automorphisms of compact Riemann surface to the point group of Carbon Tetrachloride
Department of Mathematics, DCB Girlsu2019 College, Jorhat-ASSAM (India)
Department of Mathematics, Jorhat Institute of Science & Technology, Jorhat-ASSAM
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 >.

Keyword : smooth epimorphism, point group, compact Riemann surface, AMS Subject Classification 2020: 20B25, 20B30, 20H10, 30F10
Paper Download Count : 385
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