Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

See all formats and pricing
More options …
Volume 2006, Issue 596


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.
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2006-08-16 | DOI: https://doi.org/10.1515/CRELLE.2006.058


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Christian MAIRE
Kyushu Journal of Mathematics, 2014, Volume 68, Number 2, Page 359
Nigel Boston and Rafe Jones
Geometriae Dedicata, 2007, Volume 124, Number 1, Page 27
Christian Maire
Mathematische Zeitschrift, 2011, Volume 267, Number 3-4, Page 887

Comments (0)

Please log in or register to comment.
Log in