Algebraic Properties of 〖PGL〗_2 (C) for Long Exact Fibration Sequence with Sporadic Extensions

Deep Bhattacharjee

Scientific Researcher, INS Research, Department of Geometry & Topology, India Programme Head, Electro – Gravitational Space Propulsion Laboratory, India Research Assistant, CXAI Technologies Ltd., Cyprus

Vol: 13, Issue: 2, 2023

Receiving Date: 2023-02-19 Acceptance Date:


Publication Date:


Download PDF


A concise formulation is given regarding the constructions of the group 〖PGL〗_2 (C) with its related algebraic properties with intertwined topological aspects in the long exact fibration sequences as considered over homotopy and higher order homotopy groups with further extension to sporadic groups including the monster group formulations.

Keywords: Lie Groups; Homotopy


  1. QUADRATIC EQUATIONS OF PROJECTIVE PGL2(C)-VARIETIES. (n.d.). J. Math. Comput. Sci. 3 (2013), No. 3, 808-822.
  2. n,d. (n.d.). École Normale Supérieure De Lyon.
  3. Kobayashi, Z. (1986). Automorphisms of finite order of the affine Lie algebra $A^{(1)}_{1}$. Tsukuba Journal of Mathematics.
  4. Bhattacharjee, D. (2023b). Instability in the Linkage of Topological Spaces Due to Background Ghosts. EasyChair Preprint No. 9961.
  5. Ding, C., Tang, C., & Tonchev, V. D. (2021). The projective general linear group $${\mathrm {PGL}}(2,2^m)$$ and linear codes of length $$2^m+1$$. Designs, Codes and Cryptography.
  6. Bhattacharjee, N. D., Roy, N. R., & Sadhu, N. J. (2022c). HOMOTOPY GROUP OF SPHERES, HOPF FIBRATIONS AND VIL-LARCEAU CIRCLES. EPRA International Journal of Research & Development, 57–64.
  7. Boya, L. J. (2011). Introduction to Sporadic Groups. Symmetry Integrability and Geometry-methods and Applications.
  8. Bump, D. (2004). Lie Groups. Springer Science & Business Media.
  9. Hsiang, W. Y. (2000). Lectures on Lie Groups. World Scientific.
  10. Bhattacharjee, D. (2022j). Establishing Equivariant Class [O] for Hyperbolic Groups. Asian Research Journal of Mathematics, 362–369.
  11. Bae, J., Harvey, J. A., Lee, K., Lee, S., & Rayhaun, B. C. (2021). Conformal Field Theories with Sporadic Group Symmetry. Communications in Mathematical Physics, 388(1), 1–105.
  12. Conway, J.H., Curtis, R.T., Norton, S.P., Parker, R.A., Wilson, R.A.: The ATLAS of finite groups. Oxford University Press, Oxford (1985)
  13. A001228 - OEIS. (n.d.-b).
  14. A001228 - OEIS. (n.d.).

Disclaimer: All papers published in IJRST will be indexed on Google Search Engine as per their policy.