We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.
","abstract_html":"<p>We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m<sup>*</sup><sup>n</sup> and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2<sup>*</sup><sup>n</sup>: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M<sub>11</sub> and M<sub>11</sub>, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.</p>","abstract_has_math":false,"creators":["Baccari, Kevin J"],"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":"2015-06-01T07:00:00Z","date_published":"2015-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:53Z","subjects":["progenitors","MAGMA","Iwasawa's","Double Coset Enumeration","Isomorphism Type","Algebra"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/224","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":["Baccari, Kevin J"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2015-05-21T07:00:00Z"]},{"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":["progenitors","MAGMA","Iwasawa's","Double Coset Enumeration","Isomorphism Type","Algebra"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/224"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.
"]},{"key":"dc:title","label":"Title","values":["Homomorphic Images And Related Topics"]}]}],"canonical_facts":{"dc:contributor":["Hasan, Zahid"],"dc:creator":["Baccari, Kevin J"],"dc:date.available":["2015-05-21T07:00:00Z"],"dc:description.abstract":["We will explore progenitors extensively throughout this project. The progenitor, developed by Robert T Curtis, is a special type of infinite group formed by a semi-direct product of a free group m*n and a transitive permutation group of degree n. Since progenitors are infinite, we add necessary relations to produce finite homomorphic images. Curtis found that any non-abelian simple group is a homomorphic image of a progenitor of the form 2*n: N. In particular, we will investigate progenitors that generate two of the Mathieu sporadic groups, M11 and M11, as well as some classical groups. We will prove their existences a variety of different ways, including the process of double coset enumeration, Iwasawa's Lemma, and linear fractional mappings. We will also investigate the various techniques of finding finite images and their corresponding isomorphism types.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/224"],"dc:subject":["progenitors","MAGMA","Iwasawa's","Double Coset Enumeration","Isomorphism Type","Algebra"],"dc:title":["Homomorphic Images And Related Topics"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:53Z"}