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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2006, Issue 596

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Mild pro-p-groups and Galois groups of p-extensions of ℚ

John Labute
  • Montreal; Department of Mathematics and Statistics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal QC H3A 2K6, Canada.
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Published Online: 2006-08-16 | DOI: https://doi.org/10.1515/CRELLE.2006.058

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 = G S(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 pS.

About the article

Received: 2005-01-07

Revised: 2005-05-18

Published Online: 2006-08-16

Published in Print: 2006-07-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2006, Issue 596, Pages 155–182, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2006.058.

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