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Title:Maximal 2-Extensions of Number Fields With Limited Ramification
Author(s):Perry, David Michael
Doctoral Committee Chair(s):Boston, Nigel
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
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.
Issue Date:1999
Description:80 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1999.
Other Identifier(s):(MiAaPQ)AAI9953108
Date Available in IDEALS:2015-09-28
Date Deposited:1999

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