Geodesic
Divisibility in certain automorphism groups
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 865-875 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 06F15, 20B27
Keywords: totally ordered groups; ordered automorphisms; divisible groups; archimedean rank 
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Lafuente-Rodríguez, Ramiro H. Divisibility in certain automorphism groups. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 865-875. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a6/

[1] The Black Swamp Problem Book. Maintained by W. C. Holland at Bowling Green State University, Bowling Green, OH.

[2] V. Bludov: (to appear). | Zbl

[3] P. F. Conrad: Extensions of ordered groups. Proc. American Math. Soc. 6 (1955), 516–528. | DOI | MR | Zbl

[4] P. F. Conrad: The group of order preserving automorphisms of an ordered abelian group. Proc. American Math. Soc. 9 (1958), 382–389. | DOI | MR | Zbl

[5] M. R. Darnel: Theory of Lattice-Ordered Groups. Pure and Applied Math. 187, Marcel Dekker, 1995. | MR | Zbl

[6] O. Hölder: Die Axiome der Quantität und die Lehre vom Maß. Ber. Verh. Sachs. Ges. Wiss., Leipzig Math.-Phys. Cl. 53 (1901), 1–64.

[7] W. C. Holland: Extensions of Ordered Algebraic Structures. Ph.D. Thesis, Tulane University, 1961.

[8] W. C. Holland: Transitive lattice-ordered permutation groups. Math. Zeitschr. 87 (1965), 420–433. | DOI | MR | Zbl

[9] B. H. Neumann: On ordered groups. American J. Math. 71 (1949), 1–18. | DOI | MR | Zbl