Bounds of the Group of Automorphisms of Compact Riemann Surface With Reference To The Point Group of Sulphur Molecule

eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences October, 2017 29 10 303 308 http://dx.doi.org/10.22147/jusps-B/291008 862 article Bounds of the Group of Automorphisms of Compact Riemann Surface With Reference To The Point Group of Sulphur Molecule MOLOYA BHUYAN 1 CHANDRA CHUTIA (chutia_chandra12@rediffmail.com) 2 Department of Mathematics, Devi Charan Barua Girlsu2019 College, Jorhat-785001 (India) Department of Mathematics, Jorhat Institute of Science & Technology, Jorhat-785010 (India) <p style="text-align: justify;">It is observed that every finite group is isometric to the group of Automorphisms of some Compact Riemann surface of genus 􀝃(≥ 2). Also found that the group of symmetries of a non-linear molecule (point group) is an excellent example of finite groups. In this paper we have considered the point group of Sulphur molecule S8 , which is a group of order 16. Then we prove that the bounds of the order of symmetry group of Automorphisms of Compact Riemann Surface on which the point group of S8 acts as a group of Automorphism is 4(g1), and the corresponding minimum value of g is 5, associated Fuchsian Group of signature is (2,2,2,2,2).</p> https://ultraphysicalsciences.org/paper/862/ Compact Riemann Surface Fuchsian Group, Genus Group of Automorphisms Point group 1991 Mathematics Subject Classification: 20H10, 30F10, 05C10