The odd primary homology of SU(n), Sp(n) and Spin(n)-gauge groups

For an odd prime p, we calculate the mod-p homology of SU(n)-gauge groups over a simply-connected, closed 4-manifold for all n≥2. Similar calculations are obtained for the structure groups Sp(n) when n≥1 and Spin(n) for n≥3 (except for some cases when n is even and p=3).