Some naturally occurring examples of A∞-bialgebras

Let p be an odd prime. We show that when n≥3, each tensor factor E⊗Γ of H∗(Z,n;Zp) is an A∞-bialgebra with non-trivial structure. We give explicit formulas for the structure maps and the relations among them. Thus E⊗Γ is a naturally occurring A∞-bialgebra.