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 Title: Galois Groups With Restricted Ramification Author(s): Markin, Nadya Doctoral Committee Chair(s): Boston, Nigel Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: We use modular forms to come up with an infinite family of groups that can be realized with just one finite ramifying prime. Namely, we establish that ramQ (GL2( F l)) = 1 for infinitely many primes l and for all primes 7 < l < 106591. Finally, we show the nonexistence of extensions of Q of given orders unramified outside {2, infinity}. Issue Date: 2006 Type: Text Language: English Description: 63 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006. URI: http://hdl.handle.net/2142/86877 Other Identifier(s): (MiAaPQ)AAI3250286 Date Available in IDEALS: 2015-09-28 Date Deposited: 2006
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