{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86986"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86986","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Maximal 2-Extensions of Number Fields With Limited Ramification","abstract":"Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q , p = 2, S a set of two odd primes, we find a presentation of GS given certain conditions on the primes. If the primes are both congruent to 3 modulo 4, G S is semidihedral with order explicitly given. When one prime is congruent to 3, the other congruent to 1 modulo 4, each a quadratic nonresidue of the other, then GS is a modular group with order explicitly given. The first two members of another (conjectural) family of GS are found. The use of computers in determining a presentation for GS for given S is illustrated in two appendices. The final chapter discusses computational approaches to finding candidates for pro-2 groups appearing as G S in the case where K is imaginary quadratic and S = O.","abstract_html":"Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q , p = 2, S a set of two odd primes, we find a presentation of GS given certain conditions on the primes. If the primes are both congruent to 3 modulo 4, G S is semidihedral with order explicitly given. When one prime is congruent to 3, the other congruent to 1 modulo 4, each a quadratic nonresidue of the other, then GS is a modular group with order explicitly given. The first two members of another (conjectural) family of GS are found. The use of computers in determining a presentation for GS for given S is illustrated in two appendices. The final chapter discusses computational approaches to finding candidates for pro-2 groups appearing as G S in the case where K is imaginary quadratic and S = O.","abstract_has_math":false,"creators":["Perry, David Michael"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Boston, Nigel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:20:29Z","date_published":"2015-09-28T15:20:29Z","updated_at":"2026-07-22T22:26:28Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9953108"],"render_values":[{"text":"(MiAaPQ)AAI9953108","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86986","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Boston, Nigel"]},{"key":"dc:creator","label":"Author","values":["Perry, David Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:20:29Z","10000-01-01","1999"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86986","(MiAaPQ)AAI9953108"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q , p = 2, S a set of two odd primes, we find a presentation of GS given certain conditions on the primes. If the primes are both congruent to 3 modulo 4, G S is semidihedral with order explicitly given. When one prime is congruent to 3, the other congruent to 1 modulo 4, each a quadratic nonresidue of the other, then GS is a modular group with order explicitly given. The first two members of another (conjectural) family of GS are found. The use of computers in determining a presentation for GS for given S is illustrated in two appendices. The final chapter discusses computational approaches to finding candidates for pro-2 groups appearing as G S in the case where K is imaginary quadratic and S = O.","Made available in DSpace on 2015-09-28T15:20:29Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9953108.pdf: 3093782 bytes, checksum: 5148872fbf3b999a3b757394be664456 (MD5) Previous issue date: 1999","Embargo set by: Seth Robbins for item 88267 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","80 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999."]},{"key":"dc:title","label":"Title","values":["Maximal 2-Extensions of Number Fields With Limited Ramification"]}]}],"canonical_facts":{"dc:contributor":["Boston, Nigel"],"dc:creator":["Perry, David Michael"],"dc:date":["2015-09-28T15:20:29Z","10000-01-01","1999"],"dc:description":["Let K be a number field, p a rational prime, and S a finite set of primes of K, none of which lies above p. Let K S be the maximal pro-p extension of K unramified outside S, and let GS = Gal(KS/K). In the case K = Q , p = 2, S a set of two odd primes, we find a presentation of GS given certain conditions on the primes. If the primes are both congruent to 3 modulo 4, G S is semidihedral with order explicitly given. When one prime is congruent to 3, the other congruent to 1 modulo 4, each a quadratic nonresidue of the other, then GS is a modular group with order explicitly given. The first two members of another (conjectural) family of GS are found. The use of computers in determining a presentation for GS for given S is illustrated in two appendices. The final chapter discusses computational approaches to finding candidates for pro-2 groups appearing as G S in the case where K is imaginary quadratic and S = O.","Made available in DSpace on 2015-09-28T15:20:29Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9953108.pdf: 3093782 bytes, checksum: 5148872fbf3b999a3b757394be664456 (MD5) Previous issue date: 1999","Embargo set by: Seth Robbins for item 88267 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","80 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999."],"dc:identifier":["http://hdl.handle.net/2142/86986","(MiAaPQ)AAI9953108"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["Maximal 2-Extensions of Number Fields With Limited Ramification"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:28Z"}