Hostname: page-component-cb9f654ff-hqlzj Total loading time: 0 Render date: 2025-09-06T20:00:37.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphism Groups of Homogeneous Semilinear Orders: Normal Subgroups and Commutators

Published online by Cambridge University Press:  20 November 2018

M. Droste ,
W. C. Holland  and
H. D. Macpherson
M. Droste
Affiliation:
Fachbereich 6-Mathematik und Informatik, Universität GHS Essen, D-4300 Essen 1, Federal Republic of Germany
W. C. Holland
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403, USA
H. D. Macpherson
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, England
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A partially ordered set (T, ≤) is called a tree if it is semilinearly ordered, i.e. any two elements have a common lower bound but no two incomparable elements have a common upper bound, and contains an infinite chain and at least two incomparable elements. Let k ∈ ℕ. We say that a partially ordered set (T, ≤) is k-homogeneous, if each isomorphism between two k-element subsets of T extends to an automorphism of (T, ≤), and weakly k-transitive, if for any two k-element subchains of T there exists an automorphism of (T, ≤) taking one to the other.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 721 - 737
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Adeleke, S. and Neumann, P.M.. On infinite Jordan groups. Manuscript, 1987.Google Scholar
2. Ball, R.N. and Droste, M., Normal subgroups of doubly transitive automorphism groups of chains, Trans. Amer. Math Soc. 290(1985), 647–664.Google Scholar
3. Cameron, P.J., Orbits of permutation groups on unordered sets, IV: homogeneity and transitivity, J. London Math. Soc. (2)27(1983), 238–247.Google Scholar
4. Cameron, P.J., Some treelike objects, Quart. J. Math. Oxford (2)38(1987), 155–183.Google Scholar
5. Droste, M., Structure of partially ordered sets with transitive automorphism groups, Memoirs Amer. Math. Soc. 334(1985).Google Scholar
6. Droste, M., Complete embeddings of linear orderings and embeddings of lattice-ordered groups, Israel J. Math. 56(1986), 315–334.Google Scholar
7. Droste, M., Partially ordered sets with transitive automorphism groups,Proc. London Math. Soc. (3)54(1987), 517–543.Google Scholar
8. Droste, M., Holland, W.C., Macpherson, H. D., Automorphism groups of infinite semilinear orders (I), Proc. London Math. Soc. (3)58(1989), 454–478.Google Scholar
9. Droste, M., Automorphism groups of infinite semilinear orders (II), Proc. London Math. Soc. (3)58(1989), 479–494.Google Scholar
10. Fraïssé, R., Sur certains relations qui généralissent l'ordre des nombres rationnels, C.R. Acad. Sci., Paris 237(1953), 540–542.Google Scholar
11. Fraïssé, R., Theory of Relations. North Holland, Amsterdam, 1986.Google Scholar
12. Maroli, J., Tree permutation groups. Ph.D. dissertation, Bowling Green State University, 1989.Google Scholar
13. McCleary, S.H., The lattice-ordered group of automorphisms of an α-set, Pacific J. Math. 49(1973), 417–424.Google Scholar
14. Vaught, R.L., Denumerable models of complete theories, infinitistic methods. (Proceedings of the Symposium on the Foundations of Mathematics, Warsaw 1959), Pergamon, London, 1961, 303–321.Google Scholar