Free and projective crossed modules and the second homology group of a group
type: Item
instance of: scholarly article
title: Free and projective crossed modules and the second homology group of a group
zbMATH Open document ID: 0584.20039
DOI: 10.1016/0022-4049(86)90028-9
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: The purpose of this paper under review is to provide a proof of the following Theorem: Let N be a group and let \(\partial: C\to G\) be a projective crossed module with \(\partial C=N\). Then \(H_ 2N\) is isomorphic to the kernel of the induced map (ker \(\partial)\to C^{Ab}.\) \{Reviewer's remark. Using arguments similar to those used by the authors for the proof of the Theorem, the reviewer obtained the above result in Satz 2.4 of his unpublished thesis ''Verschränkte n-fache Erweiterungen von Gruppen und Cohomologie'' [Diss. ETH Nr. 5999, Eidgenössische Technische Hochschule, Zürich (1977)] in the special case where \(\partial: C\to G\) is a free crossed module. The extension form free to projective crossed modules is simple.\}
Mathematics Subject Classification ID: 20J05
zbMATH DE Number: 3935320
zbMATH Keywords: second homology group
zbMATH Keywords: free crossed module
zbMATH Keywords: projective crossed modules
author: Graham Ellis
author: Timothy Porter
reviewed by: J. Huebschmann
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90028-9
OpenAlex ID: W2088465192
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description: scientific article; zbMATH DE number 3935320