A solution of the Steenrod problem for G-Moore spaces
type: Item
instance of: scholarly article
title: A solution of the Steenrod problem for G-Moore spaces
zbMATH Open document ID: 0659.55008
DOI: 10.1007/BF00539621
author: Pierre Vogel
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: Let M be a module over a group G, and let \(k\geq 3\) be an integer. A simply-connected G-space X is called a G-Moore space of type (M,k) if \(\tilde H_ iX=0\), unless \(i=k\), and \(\tilde H_ kX\) is isomorphic to M as a G-module. In this case we say that X realizes M (in degree k). The Steenrod problem asks, under somewhat more stringent conditions, which modules M are realizable. The main theorem for this paper is the following: The following are equivalent for a finite group G: (a) Every G-module is realizable. (b) Every Sylow subgroup of G is cyclic.
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55U15
Mathematics Subject Classification ID: 18G99
Mathematics Subject Classification ID: 20J99
zbMATH DE Number: 4078260
zbMATH Keywords: cohomologically trivial
zbMATH Keywords: simply-connected G-space
zbMATH Keywords: G-Moore space
zbMATH Keywords: Steenrod problem
zbMATH Keywords: Sylow subgroup
reviewed by: Peter J. Kahn
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4078260