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The closed prime
subgroups of certain ordered permutation groups
Stephen H. McCleary |
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Vol. 31 (1969), No. 3, 745–753
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Abstract |
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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
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Milestones
Received: 19 June 1969
Published: 1 December 1969
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Authors |
| Stephen H. McCleary | |
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