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.
","abstract_html":"<p>In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2<sup>*</sup><sup>7</sup>: D<sub>14</sub>, 2<sup>*7 </sup>: (7 : 2), 2<sup>*6 </sup>: S<sub>3 </sub>x 2, 2<sup>*8</sup>: S<sub>4</sub>, 2*<sup>72</sup>: (3<sup>2</sup>:(2S<sub>4</sub>)), and 11<sup>*2</sup> :<sub>m </sub>D<sub>10</sub>. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M<sub>11</sub>, M<sub>12</sub>, the 4-fold cover of the Mathieu group M<sub>22</sub>, 2 x L<sub>2</sub>(8), and L<sub>2</sub>(13). Moreover, we have given constructions, by using the technique of double coset enumeration, for some of the images, including M<sub>11</sub> and M<sub>12</sub>. 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 L<sub>2</sub>(13) over A<sub>5</sub>, L<sub>2</sub>(8) over D<sub>14</sub>, L<sub>2</sub>(13) over D<sub>14</sub>, L<sub>2</sub>(27) over 2D<sub>14</sub>, and M<sub>11</sub> over 2S<sub>4</sub> are simple groups. All of the work presented in this thesis is original to the best of our knowledge.</p>","abstract_has_math":false,"creators":["Ramirez, Jessica Luna"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Hasan, Zahid"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-12-01T08:00:00Z","date_published":"2015-12-01T08:00:00Z","updated_at":"2026-07-24T01:52:53Z","subjects":["Group theory","Mathieu groups","linear groups","construction","Algebra"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/254","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hasan, Zahid"]},{"key":"dc:creator","label":"Author","values":["Ramirez, Jessica Luna"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-11-11T08:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts in Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Group theory","Mathieu groups","linear groups","construction","Algebra"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/254"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES"]}]}],"canonical_facts":{"dc:contributor":["Hasan, Zahid"],"dc:creator":["Ramirez, Jessica Luna"],"dc:date.available":["2015-11-11T08:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/254"],"dc:subject":["Group theory","Mathieu groups","linear groups","construction","Algebra"],"dc:title":["CONSTRUCTIONS AND ISOMORPHISM TYPES OF IMAGES"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:53Z"}