On the cohomology of pro-fusion systems

Abstract

We prove the Cartan-Eilenberg stable elements theorem and construct a Lyndon-Hochschild-Serre type spectral sequence for pro-fusion systems. As an application, we determine the continuous mod-p cohomology ring of GL 2 (Zp) for any odd prime p. H * c (BG p ) ∼ = H * c (G).