o − 2-transitive ordered permutation groups

Stephen H. McCleary

Vol. 49 (1973), No. 2, 425–429

DOI: 10.2140/pjm.1973.49.425

Abstract

The group of all automorphisms of a chain Ω forms a lattice-ordered group A (Ω) under the pointwise order. Let G be an l-subgroup of A (Ω) which is o-2-transitive, i.e., for any β < γ and σ < τ, there exists g ∈ G such that βg = σ and γg = τ. It is shown that G is a complete subgroup of A (Ω) if and only if G is completely distributive if and only if G contains an element ≠1 of bounded support. There is a discussion of the pathological groups in which these conditions are absent.

Mathematical Subject Classification

Primary: 06A55

Milestones

Received: 24 May 1973

Published: 1 December 1973