Abstract
The spaces BG2 and BDI.4/ have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces, one has the classifying spaces of the finite groups BG2.q/, for an odd prime powerq, and the exotic family of classifying spaces of 2-local finite groupsBSol.q/. In this article we compute the loop space homology of BG2.q/ ^ andBSol.q/ for all odd primesq, as Hopf algebras over the Steenrod algebra, and the associated Bockstein spectral sequences.
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