Vol. 49, No. 2, 1973

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o 2-transitive ordered permutation groups

Stephen H. McCleary

Vol. 49 (1973), No. 2, 425–429

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
Received: 24 May 1973
Published: 1 December 1973
Stephen H. McCleary