On subdirect products of free pro-\(p\) groups and Demushkin groups of infinite depth.
type: Item
instance of: scholarly article
title: On subdirect products of free pro-\(p\) groups and Demushkin groups of infinite depth.
zbMATH Open document ID: 1242.20062
author: Hamish Short
author: Dessislava H. Kochloukova
published in: Journal of Algebra
publication date: 2012-02-11T00:00:00Z
review text: A pro-\(p\) group \(G\) is said to be of type \(\text{FP}_m\) if there is a projective resolution of the trivial \(\mathbb Z_pG\)-module \(\mathbb Z_p\), where all modules up to dimension \(m\) are finitely generated. Here \(\mathbb Z_p\) is the ring of \(p\)-adic integers, and \(\mathbb Z_pG\) is the completed group algebra. In the paper under review the authors classify among others the subdirect products of free and Demushkin pro-\(p\) groups of depth \(\infty\) which have homological type \(\text{FP}_m\) for \(m\geq 2\). Although the model for these investigations is the abstract case (see the paper by \textit{M.~R.~Bridson, J. Howie, C. F. Miller III} and \textit{H. Short} [Geom. Dedicata 92, 95-103 (2002; Zbl 1048.20009)]), they note that the corresponding problem is still open for abstract groups for \(m\geq 3\).
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 6005462
zbMATH Keywords: subdirect products
zbMATH Keywords: pro-\(p\) groups
zbMATH Keywords: Demushkin groups
zbMATH Keywords: projective resolutions
zbMATH Keywords: homological finiteness conditions
reviewed by: Andrea Caranti
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.06.012
OpenAlex ID: W2014488587
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DOI: 10.1016/J.JALGEBRA.2011.06.012
description: scientific article; zbMATH DE number 6005462