Abelian subgroups of the fundamental group of a space with no conjugate points

Each Abelian subgroup of the fundamental group of a compact and locally simply connected d-dimensional length space with no conjugate points is isomorphic to Z(k) for some 0 <= k <= d. It follows from this and previously known results that each solvable subgroup of the fundamental group is a Bieberbach group. In the Riemannian setting, this may be proved using a novel property of the asymptotic norm of each Abelian subgroup.