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Mild pro-p-groups and Galois groups of p-extensions of ℚ
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John Labute
Published/Copyright:
August 16, 2006
Abstract
In this paper we introduce a new class of finitely presented pro-p-groups G of cohomological dimension 2 called mild groups. If d(G), r(G) are respectively the minimal number of generators and relations of G, we give an infinite family of mild groups G with r(G) ≧ d(G) and d(G) ≧ 2 arbitrary. These groups can be constructed with G/[G, G] finite, answering a question of Kuzmin. If G = GS(p) is the Galois group of the maximal p-extension of ℚ unramified outside a finite set of primes S and p ≠ 2, we show that G is mild for a co-final class of sets S, even in the case p ∉ S.
Received: 2005-01-07
Revised: 2005-05-18
Published Online: 2006-08-16
Published in Print: 2006-07-01
© Walter de Gruyter
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Articles in the same Issue
- Free boundary regularity below the continuous threshold: 2-phase problems
- Lp-theory of the Navier-Stokes flow in the exterior of a moving or rotating obstacle
- The Kirillov-Reshetikhin conjecture and solutions of T-systems
- Hyperbolicity of nodal hypersurfaces
- Unipotent orbits and local L-functions
- Circular sets of prime numbers and p-extensions of the rationals
- The μ-invariant of anticyclotomic L-functions of imaginary quadratic fields
- Zum Hauptsatz von C. Jordan über ganzzahlige Darstellungen endlicher Gruppen
- Mild pro-p-groups and Galois groups of p-extensions of ℚ
- The fifty-two icosahedral solutions to Painlevé VI
- Residue currents of holomorphic morphisms
