SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS

Author

Connie CoronaFollow

Date of Award

12-2021

Document Type

Thesis

Degree Name

Master of Arts in Mathematics

Department

Mathematics

First Reader/Committee Chair

Hasan, Zahid

Abstract

In this thesis, we have presented our discovery of original symmetric presentations of a number of non-abelian simple groups, including several sporatic groups, linear groups, and classical groups.

We have constructed, using our technique of double coset enumeration, J2, M₁₂, J₁, PSU(3, 3):2, M₁₁, A₁₀, S(4,3), M₂₂:2, PSL(3, 4), S₆, 2:S₅, 2:PSL(3, 4) as homomorphic images of the involutory progenitors 2^*32:(2⁵:A₅), 2^*110: PSL(2, 11), 2^*5:A₅, 3^*4:D₈, 2^*110:PSL(2, 11), 2^*42:PSL(2, 7), 2^*21:(2XA₇), 2^*40:(24:(5:3)), 2^*15: A₇, respectively and S₆, S₈, J₂, M₁₂:2, as homomorphic images of the monomial progenitors 2^*5:A₅, 2^*42:PSL(2, 7), 2^*18:(3:A₆), 2^*8:(2³:(4:2)), 2^*5:(5:4) respectively. In addition we have given isomorphism types of all images that were discovered.

Recommended Citation

Corona, Connie, "SYMMETRIC REPRESENTATIONS OF FINITE GROUPS AND RELATED TOPICS" (2021). Electronic Theses, Projects, and Dissertations. 1350.
https://scholarworks.lib.csusb.edu/etd/1350