totally ordered groups; ordered automorphisms; divisible groups; archimedean rank
We study solvability of equations of the form $x^n=g$ in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.
 The Black Swamp Problem Book. Maintained by W. C. Holland at Bowling Green State University, Bowling Green, OH.
 M. R. Darnel: Theory of Lattice-Ordered Groups
. Pure and Applied Math. 187, Marcel Dekker, 1995. MR 1304052
| Zbl 0810.06016
 O. Hölder: Die Axiome der Quantität und die Lehre vom Maß. Ber. Verh. Sachs. Ges. Wiss., Leipzig Math.-Phys. Cl. 53 (1901), 1–64.
 W. C. Holland: Extensions of Ordered Algebraic Structures. Ph.D. Thesis, Tulane University, 1961.