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