{"id":{"repo_id":"byu","oai_identifier":"oai:scholarsarchive.byu.edu:etd-1161"},"canonical_url":"https://search.dev.ndltd.org/etd/byu/oai:scholarsarchive.byu.edu:etd-1161","repository":{"repo_id":"byu","name":"Brigham Young University","base_url":"https://scholarsarchive.byu.edu/do/oai/"},"display":{"title":"PSL(2,7)-Extensions with Certain Ramification at Two Primes","abstract":"We conduct a parallel Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2<p<104. The number field we seek will satisfy certain criteria allowing for refinement of a conjecture of Ash, Doud, and Pollack. In the course of our search we prove that the smallest p for which such an example occurs is p=31 and that the next possible example occurs at p=103.","abstract_html":"We conduct a parallel Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2<p<104. The number field we seek will satisfy certain criteria allowing for refinement of a conjecture of Ash, Doud, and Pollack. In the course of our search we prove that the smallest p for which such an example occurs is p=31 and that the next possible example occurs at p=103.","abstract_has_math":false,"creators":["Simpson, Glen E."],"institution":"Brigham Young University - Provo","degree_name":"MS","degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":null,"date_issued":"","date_published":null,"updated_at":"2026-07-24T01:27:25Z","subjects":["Galois Representation","number field","Hunter search","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarsarchive.byu.edu/etd/162","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Simpson, Glen E."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2004-07-02T07:00:00Z"]},{"key":"dc:publisher","label":"Institution","values":["Brigham Young University - Provo"]},{"key":"dc:type","label":"Dc Type","values":["Selected Project"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Galois Representation","number field","Hunter search","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarsarchive.byu.edu/etd/162","https://scholarsarchive.byu.edu/context/etd/article/1161/viewcontent/ETD_CISOPTR_181.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Physical and Mathematical Sciences; Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["We conduct a parallel Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2<p<104. The number field we seek will satisfy certain criteria allowing for refinement of a conjecture of Ash, Doud, and Pollack. In the course of our search we prove that the smallest p for which such an example occurs is p=31 and that the next possible example occurs at p=103."]},{"key":"dc:format","label":"Dc Format","values":["application:pdf"]},{"key":"dc:source","label":"Dc Source","values":["Brigham Young University - Provo"]},{"key":"dc:title","label":"Title","values":["PSL(2,7)-Extensions with Certain Ramification at Two Primes"]}]}],"canonical_facts":{"dc:creator":["Simpson, Glen E."],"dc:date":["2004-07-02T07:00:00Z"],"dc:description":["Physical and Mathematical Sciences; Mathematics"],"dc:description.abstract":["We conduct a parallel Hunter search in order to find a degree 7 number field K ramified at primes q and p with discriminant d(K)=q^6 p^2 where q=11 and 2<p<104. The number field we seek will satisfy certain criteria allowing for refinement of a conjecture of Ash, Doud, and Pollack. In the course of our search we prove that the smallest p for which such an example occurs is p=31 and that the next possible example occurs at p=103."],"dc:format":["application:pdf"],"dc:identifier":["https://scholarsarchive.byu.edu/etd/162","https://scholarsarchive.byu.edu/context/etd/article/1161/viewcontent/ETD_CISOPTR_181.pdf"],"dc:language":["English"],"dc:publisher":["Brigham Young University - Provo"],"dc:source":["Brigham Young University - Provo"],"dc:subject":["Galois Representation","number field","Hunter search","Mathematics"],"dc:title":["PSL(2,7)-Extensions with Certain Ramification at Two Primes"],"dc:type":["Selected Project"],"thesis:degree_name":["MS"]},"updated_at":"2026-07-24T01:27:25Z"}