The main goal of this project is to present my investigation of finite images of the progenitor 2^(*n) : N for various N and several values of n. We construct each image by using the technique of double coset enumeration and give a proof of the isomorphism type of the image. We obtain the group 7^2: D_6 as a homomorphic image of the progenitor 2^(*14) : D_14, we obtain the group 2^4 : (5 : 4) as a homomorphic image of the progenitor 2^(*5) : (5 : 4), we obtain the group (10 x10) : ((3 x 4) : 2) as a homomorphic image of the progenitor 2^(*15) : (15x4), we obtain the group PGL(2; 7) as a homomorphic image of the progenitor 2^7 : D_14, we obtain the group S_6 as a homomorphic image of the progenitor 2^5 : (5 : 4), and we obtain the group S_7 as a homomorphic image of the progenitor 2^(*15) : (15 : 4). Also, have given some unsuccessful progenitors.
| Identifer | oai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1667 |
| Date | 01 December 2017 |
| Creators | Yeo, Michelle SoYeong |
| 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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