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CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES

In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2*7: D14, 2*7 : (7 : 2), 2*6 : S3 x 2, 2*8: S4, 2*72: (32:(2S4)), and 11*2 :m D10. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M11, M12, the 4-fold cover of the Mathieu group M22, 2 x L2(8), and L2(13). Moreover, we have given constructions, by using the technique of double coset enumeration, for some of the images, including M11 and M12. We have given proofs, either by hand or computer-based, of the isomorphism type of each image. In addition, we use Iwasawa's Lemma to prove that L2(13) over A5, L2(8) over D14, L2(13) over D14, L2(27) over 2D14, and M11 over 2S4 are simple groups. All of the work presented in this thesis is original to the best of our knowledge.

Identiferoai:union.ndltd.org:csusb.edu/oai:scholarworks.lib.csusb.edu:etd-1288
Date01 December 2015
CreatorsRamirez, Jessica Luna
PublisherCSUSB ScholarWorks
Source SetsCalifornia State University San Bernardino
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceElectronic Theses, Projects, and Dissertations

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