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Representations of free lattice-ordered groups

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Abstract

We show for any uncountable cardinal η that the free groupG η of rank η has a linear right ordering on which the natural action of the free lattice-ordered groupF η of rank η is faithful and pathologically 2-transitive. As a consequence, we obtain results on the root system of prime subgroups ofF η . This generalizes previous results of McCleary which required the generalized continuum hypothesis and η to be regular.

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Author notes

  1. Manfred Droste

    Present address: Abteilung Mathematik, Technische Universität Dresden, 01062, Dresden, Germany

Authors and Affiliations

  1. Fachbereich 6, Mathematik und Informatik, Universität GHS Essen, 45117, Essen, Germany

    Manfred Droste

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  1. Manfred Droste
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Communicated by K. Keimel

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Droste, M. Representations of free lattice-ordered groups. Order 10, 375–381 (1993). https://doi.org/10.1007/BF01108831

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  • DOI: https://doi.org/10.1007/BF01108831

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