Free and projective crossed modules and the second homology group of a group
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to those used by the authors for the proof of the Theorem, the reviewer obtained the above result in Satz 2.4 of his unpublished thesis ''Verschränkte n-fache Erweiterungen von Gruppen und Cohomologie'' [Diss.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.\}
scientific article; zbMATH DE number 3935320