SYMMETRIC PRESENTATIONS AND RELATED TOPICS

Author

Mashael U. Alharbi, California State University - San BernardinoFollow

Date of Award

3-2015

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 symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M₁₂. We have given several progenitors, permutation and monomial, including 2*⁴:(2²:3), 2*⁵:D₁₀, 2*⁸:((4X2).D₄), 3*⁷:_m L₂(7), 2*⁶:(Z₃ wr Z₂), and 2*²⁴: (2^. A₅) and their homomorphic images which include 4.(M₁₂:2), the group of automorphisms of M₁₂ and several classical groups. We have given the isomorphism type of each of the group mentioned in the thesis. In each case, a proof of the isomorphism type is provided, either computer-based or by hand. In addition, by hand constructions, using the technique of double coset enumeration, are given for the groups L₂(11)X3, L₂(11), PGL₂(11), S₅,(A₅XA₅):4, A₇, and 3⁷:L₂(7).

Recommended Citation

Alharbi, Mashael U., "SYMMETRIC PRESENTATIONS AND RELATED TOPICS" (2015). Electronic Theses, Projects, and Dissertations. 128.
https://scholarworks.lib.csusb.edu/etd/128