  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 $\mathbb{Z}^k$ for some $0 \leq k \leq d$. 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.
