Abstract
dc:description.abstract<p>In this thesis, we have presented our discovery of symmetric presentations of a number of non-abelian simple groups, including the Mathieu group M<sub>12</sub>. We have given several progenitors, permutation and monomial, including 2*<sup>4</sup>:(2<sup>2</sup>:3), 2*<sup>5</sup>:D<sub>10</sub>, 2*<sup>8</sup>:((4X2).D<sub>4</sub>), 3*<sup>7</sup>:<sub>m</sub> L<sub>2</sub>(7), 2*<sup>6</sup>:(Z<sub>3</sub> wr Z<sub>2</sub>), and 2*<sup>24</sup>: (2<sup>.</sup> A<sub>5</sub>) and their homomorphic images which include 4.(M<sub>12</sub>:2), the group of automorphisms of M<sub>12</sub> 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 L<sub>2</sub>(11)X3, L<sub>2</sub>(11), PGL<sub>2</sub>(11), S<sub>5</sub>,(A<sub>5</sub>XA<sub>5</sub>):4, A<sub>7</sub>, and 3<sup>7</sup>:L<sub>2</sub>(7).</p>
Degree
thesis:*- Name thesis:degree_name
- Master of Arts in Mathematics
- Level thesis:degree_level
- Thesis
- Discipline thesis:degree_discipline
- Mathematics
- Year dc:date.available
- 2015
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Alharbi, Mashael U
- Contributors dc:contributor
-
- Hasan, Zahid
Subjects
dc:subject × 2Identifiers
dc:identifier.*- Repository record dc:identifier
- https://scholarworks.lib.csusb.edu/etd/128
- OAI identifier oai:identifier
- oai:scholarworks.lib.csusb.edu:etd-1140