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https://hdl.handle.net/2142/86877
Description
Title
Galois Groups With Restricted Ramification
Author(s)
Markin, Nadya
Issue Date
2006
Doctoral Committee Chair(s)
Boston, Nigel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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}.
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