In this project, we demonstrate our discovery of original symmetric presentations and constructions of important groups, including nonabelian simple groups, and groups that have these as factor groups. The target nonabelian simple groups include alternating, linear, and sporadic groups. We give isomorphism types for each finite homomorphic image that has been found. We present original symmetric presentations of $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ as homomorphism images of the progenitors $2^{*20}$ $:$ $A_{5}$, $2^{*10}$ $:$ $PGL(2,9)$, $2^{*10}$ $:$ $Aut(A_{6})$, $2^{*10}$ $:$ $A_{6}$, $2^{*10}$ $:$ $A_{5}$, and $2^{*24}$ $:$ $S_{5}$, respectively. We also construct $M_{12}$, $M_{21}:(2 \times 2)$, $L_{3}(4):2^2$, $L_{3}(4):2^2$, $2:^{\cdot}L_{3}(4):2$, $S(4,3)$, and $S_{7}$ over $A_{5}$, $PGL(2,9)$, $Aut(A_{6})$, $A_{6}$, $A_{5}$, and $S_{5}$, respectively, using our technique of double coset enumeration. All of the symmetric presentations given are original to the best of our knowledge.
| Identifer | oai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1872 |
| Date | 01 December 2018 |
| Creators | Seager, Charles |
| 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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