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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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Volume 2011, Issue 658


Strongly free sequences and pro-p-groups of cohomological dimension 2

Patrick Forré
Published Online: 2011-04-14 | DOI: https://doi.org/10.1515/crelle.2011.067


There are a lot of arithmetic consequences if a Galois group of a number field is of cohomological dimension ≦ 2 (cf. [Schmidt, J. reine angew. Math. 596: 115–130, 2006], [Schmidt, Doc. Math. 12: 441–471, 2007], [Schmidt, J. reine angew. Math. 640: 203–235, 2010]). But with class field theory we only have an approximate description of the relators of such groups, which makes it difficult to determine the cohomological dimension. There are several criteria (cf. [Labute, Math. 596: 155–182, 2006], [Labute and Mináč, Mild pro-2-groups and 2-extensions of ℚ with restricted ramification, 2009]) on the so called linking numbers to get cd ≦ 2. The techniques in these papers use Lie algebra theory which become much more complicated for pro-2-groups. Here we will give a more simple and direct proof of the same algebraic criteria for a pro-p-group to be of cd ≦ 2 including the case p = 2.

About the article

Received: 2009-12-22

Revised: 2010-05-06

Published Online: 2011-04-14

Published in Print: 2011-09-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011, Issue 658, Pages 173–192, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2011.067.

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