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Each Abelian subgroup of the fundamental group of a compact and locallysimply connected $d$-dimensional length space with no conjugate points isisomorphic to $\mathbb{Z}^k$ for some $0 \leq k \leq d$. It follows from thisand previously known results that each solvable subgroup of the fundamentalgroup is a Bieberbach group. In the Riemannian setting, this may be provedusing a novel property of the asymptotic norm of each Abelian subgroup.

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