Vol. 31, No. 3, 1969

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The closed prime subgroups of certain ordered permutation groups

Stephen H. McCleary

Vol. 31 (1969), No. 3, 745–753

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
Received: 19 June 1969
Published: 1 December 1969
Stephen H. McCleary