The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w | pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive groups in 6,10,12, and 18 letters. Which led to identify some appealing groups for this project, such as Janko group J1, Symplectic groups S(4,3) and S(6,2), Mathieu group M12 and some linear groups such as PGL2(7) and L2(11) . With this information, we performed double coset enumeration on some of our findings, M12 over L_2(11) and L_2(31) over D15. We will also prove their isomorphism types with the help of the Jordan-Holder theorem, which aids us in defining the make up of the group. Some examples that we will encounter are the extensions of L_2(31)(center) 2 and A5:2^2.
| Identifer | oai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1817 |
| Date | 01 June 2018 |
| Creators | Baccari, Angelica |
| Publisher | CSUSB ScholarWorks |
| Source Sets | California State University San Bernardino |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses, Projects, and Dissertations |
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