. Abstract: This talk is a report of work in progress. In her thesis, Ainhoa Berciano gave explicit formulas for the A-infinity coalgebra structure maps on the mod p homology of K(Z,n). Since H_*(Z,n;Z_p) is a Hopf algebra, it is natural to ask whether the higher order A-infinity coalgebra operations are in some sense compatible with the Pontryagin product. In this talk we make the notion of "higher order compatibility" precise and verify that the compatibility relation holds in low dimensions when p=3. If compatiility holds in all dimensions, and we expect it does, H_*(Z,n;Z_3) is the first naturally occurring example of an A-infinity bialgebra whose internal structure is explicitly defined and whose structure relations are well-understood.