Vol. 31, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
The closed prime subgroups of certain ordered permutation groups

Stephen H. McCleary

Vol. 31 (1969), No. 3, 745–753
Abstract

The group G = A(Ω) of all order-preserving permutations of a chain Ω becomes a lattice-ordered group when ordered pointwise, i.e., f g if and only if βf βg for all β Ω. Lloyd showed that for each ω Ω, the stabilizer subgroup Gω = {g G|ωg = ω} is a closed prime subgroup of G. Our main result (Theorem 11) states that besides G itself, these subgroups, together with the stabilizer subgroups of Dedekind cuts of Ω, comprise all of the closed prime subgroups of G.

Mathematical Subject Classification
Primary: 06.75
Milestones
Received: 19 June 1969
Published: 1 December 1969
Authors
Stephen H. McCleary