Qd(\(p\))-free rank two finite groups act freely on a homotopy product of two spheres (Q860420)

The author considers the Benson and Carlson conjecture, which states that for any finite group \(G\), rk\((G)=\)h\((G)\), where rk\((G)=\max_{p: prime}\{rk_p(G)\}\), \(rk_p(G)\) is the largest rank of an elementary abelian \(p\)-subgroup of \(G\), and h\((G)\) is the minimal integer \(k\) such that \(G\) acts freely on a finite CW-complex homotopic to \(S^{n_1}\times S^{n_2}\times\cdots\times S^{n_k}\). For \(G\) a rank one group, the conjecture is a direct consequence of Swan's theorem. For \(G\) with rk\((G)=2\), the conjecture has been proven by Adem and Smith. The paper under review gives a refinement for the case rk\((G)=2\), and the main result is that rank two groups that are Qd\((p)\)-free act freely on a finite homotopy product of two spheres.