| Title:
|
Divisibility in certain automorphism groups (English) |
| Author:
|
Lafuente-Rodríguez, Ramiro H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
865-875 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
totally ordered groups |
| Keyword:
|
ordered automorphisms |
| Keyword:
|
divisible groups |
| Keyword:
|
archimedean rank |
| MSC:
|
06F15 |
| MSC:
|
20B27 |
| idZBL:
|
Zbl 1174.06339 |
| idMR:
|
MR2356286 |
| . |
| Date available:
|
2009-09-24T11:50:07Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128212 |
| . |
| Reference:
|
[1] : The Black Swamp Problem Book.Maintained by W. C. Holland at Bowling Green State University, Bowling Green, OH. |
| Reference:
|
[2] V. Bludov: .(to appear). Zbl 1167.06010 |
| Reference:
|
[3] P. F. Conrad: Extensions of ordered groups.Proc. American Math. Soc. 6 (1955), 516–528. Zbl 0066.01702, MR 0073605, 10.1090/S0002-9939-1955-0073605-0 |
| Reference:
|
[4] P. F. Conrad: The group of order preserving automorphisms of an ordered abelian group.Proc. American Math. Soc. 9 (1958), 382–389. Zbl 0098.01901, MR 0102549, 10.1090/S0002-9939-1958-0102549-3 |
| Reference:
|
[5] M. R. Darnel: Theory of Lattice-Ordered Groups.Pure and Applied Math. 187, Marcel Dekker, 1995. Zbl 0810.06016, MR 1304052 |
| Reference:
|
[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. |
| Reference:
|
[7] W. C. Holland: Extensions of Ordered Algebraic Structures.Ph.D. Thesis, Tulane University, 1961. |
| Reference:
|
[8] W. C. Holland: Transitive lattice-ordered permutation groups.Math. Zeitschr. 87 (1965), 420–433. Zbl 0147.01204, MR 0178052, 10.1007/BF01111722 |
| Reference:
|
[9] B. H. Neumann: On ordered groups.American J. Math. 71 (1949), 1–18. Zbl 0031.34201, MR 0028312, 10.2307/2372087 |
| . |
