Irreducible 4-manifolds with abelian non-cyclic fundamental group of small rank

In this paper we construct several irreducible 4-manifolds, both small and arbitrarily large, with abelian non-cyclic fundamental group. The manufacturing procedure allows us to fill in numerous points in the geography plane of symplectic manifolds with π1=Z⊕Z,Z⊕Zp and Zq⊕Zp (gcd(p,q)≠1). We then study the botany of these points for π1=Zp⊕Zp.