A solution of the Steenrod problem for G-Moore spaces
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.
scientific article; zbMATH DE number 4078260