University of Illinois Urbana-Champaign

Maximal 2-Extensions of Number Fields With Limited Ramification

Perry, David Michael

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Description

Title
Maximal 2-Extensions of Number Fields With Limited Ramification
Author(s)
Perry, David Michael
Issue Date
1999
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
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.
Graduation Semester
1999
Type of Resource
text
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http://hdl.handle.net/2142/86986

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