Abstract
We show that divisibility fails in a wide spectrum of periodic lattice-ordered permutation groups. The methods are applied to the six previously known ‘pathological’ doubly transitive groups represented on ℝ or on ℝ+, and only two of these groups turn out to be divisible.
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Hurd, S. Divisibility in O-primitive lattice-ordered permutation groups. Order 3, 195–205 (1986). https://doi.org/10.1007/BF00390109
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DOI: https://doi.org/10.1007/BF00390109