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).
| Identifer | oai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1140 |
| Date | 01 March 2015 |
| Creators | Alharbi, Mashael U |
| Publisher | CSUSB ScholarWorks |
| Source Sets | California State University San Bernardino |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses, Projects, and Dissertations |
Page generated in 0.0014 seconds