Abstract
In this note we discuss permutation groups (G, Ω) in which the set Ω admits aG-invariant order. By aG-invariant partial order (G-partial order) we mean a partial order < of Ω such that α<β implies αg<βg, for all α and β in Ω andg inG. If the set Ω admits aG-partial order which is a total order, then (G, Ω) is an O-permutation group (orderable permutation group).
The main concern of this paper is the development of a foundation for partially ordered permutation groups analogous to the existing one for partially ordered groups, as found in Fuchs [2].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Boto Mura and A. Rhemtulla (1977)Orderable Groups, Lecture Notes in Pure and Applied Mathematics, Vol. 27, Marcel Dekker.
L. Fuchs (1963)Partially Ordered Algebraic Systems, Pergamon Press, New York.
A. M. W. Glass (1967)Ordered Permutation Groups, Bowling Green State University.
H. A. Hollister (1965) Contributions to the theory of partially ordered groups, Doctoral Dissertation, University of Michigan.
S. H. McCleary (1972) O-primitive ordered permutation groups,Pacific J. Math. 40, 349–372.
H. Wielandt (1967)Unendliche Permutationsgruppen, York University, Toronto, Ontario, Canada.
Author information
Authors and Affiliations
Additional information
Communicated by R. P. Dilworth
Rights and permissions
About this article
Cite this article
Putt, H.L. Partially ordered permutation groups. Order 1, 173–185 (1984). https://doi.org/10.1007/BF00565652
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00565652