In this thesis we have investigated permutation and monomial progenitors of the form p^*n:N (p=2,3,5,...) and p^*n:_m N (p=3,5,7,...) respectively. We have discovered new symmetric presentations of several finite nonabelian simple groups including linear groups, unitary groups, orthogonal groups, and sporadic groups. We have constructed interesting groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over finite fields.
","abstract_html":"<p>In this thesis we have investigated permutation and monomial progenitors of the form p^*n:N (p=2,3,5,...) and p^*n:_m N (p=3,5,7,...) respectively. We have discovered new symmetric presentations of several finite nonabelian simple groups including linear groups, unitary groups, orthogonal groups, and sporadic groups. We have constructed interesting groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over finite fields.</p>","abstract_has_math":false,"creators":["Gomez, David R, Jr"],"institution":null,"degree_name":"Master of Arts in Mathematics","degree_level":"Restricted Thesis: Campus only access","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["DR. ZAHID HASAN"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-06-01T07:00:00Z","date_published":"2014-06-01T07:00:00Z","updated_at":"2026-07-24T01:52:37Z","subjects":["symmetric presentations","double coset enumeration","progenitor","Algebra"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.lib.csusb.edu/etd/96","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["DR. ZAHID HASAN"]},{"key":"dc:creator","label":"Author","values":["Gomez, David R, Jr"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-05-16T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Restricted Thesis: Campus only access"]},{"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":["symmetric presentations","double coset enumeration","progenitor","Algebra"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.lib.csusb.edu/etd/96"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we have investigated permutation and monomial progenitors of the form p^*n:N (p=2,3,5,...) and p^*n:_m N (p=3,5,7,...) respectively. We have discovered new symmetric presentations of several finite nonabelian simple groups including linear groups, unitary groups, orthogonal groups, and sporadic groups. We have constructed interesting groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over finite fields.
"]},{"key":"dc:title","label":"Title","values":["SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS"]}]}],"canonical_facts":{"dc:contributor":["DR. ZAHID HASAN"],"dc:creator":["Gomez, David R, Jr"],"dc:date.available":["2014-05-16T07:00:00Z"],"dc:description.abstract":["In this thesis we have investigated permutation and monomial progenitors of the form p^*n:N (p=2,3,5,...) and p^*n:_m N (p=3,5,7,...) respectively. We have discovered new symmetric presentations of several finite nonabelian simple groups including linear groups, unitary groups, orthogonal groups, and sporadic groups. We have constructed interesting groups found using the technique of double coset enumeration and found the isomorphic types of the numerous groups that appeared as homorphic images. These include the sympletic group, S_4(5) and the Janko groups, J_2 and J_1 which were found using a variety of different control groups over finite fields.
"],"dc:identifier":["https://scholarworks.lib.csusb.edu/etd/96"],"dc:subject":["symmetric presentations","double coset enumeration","progenitor","Algebra"],"dc:title":["SYMMETRIC PRESENTATIONS AND CONSTRUCTIONS"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Restricted Thesis: Campus only access"],"thesis:degree_name":["Master of Arts in Mathematics"]},"updated_at":"2026-07-24T01:52:37Z"}