The connective K-theory of the Eilenberg-MacLane space K(Z/p,2)

We compute ku^(K(Z/p,2)) and ku_(K(Z/p,2)), the connective KU-cohomology and connective KU-homology groups of the mod-p Eilenberg-MacLane space K(Z/p,2), using the Adams spectral sequence. We obtain a striking interaction between h_0-extensions and exotic extensions. The mod-p connective KU-cohomology groups, computed elsewhere, are needed in order to establish higher differentials and exotic extensions in the integral groups.