Representations of free lattice-ordered groups |
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| Authors: | Manfred Droste |
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| Institution: | (1) Fachbereich 6, Mathematik und Informatik, Universität GHS Essen, 45117 Essen, Germany;(2) Present address: Abteilung Mathematik, Technische Universität Dresden, 01062 Dresden, Germany |
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| Abstract: | We show for any uncountable cardinal  that the free groupG
of rank has a linear right ordering on which the natural action of the free lattice-ordered groupF
of rank is faithful and pathologically 2-transitive. As a consequence, we obtain results on the root system of prime subgroups ofF
. This generalizes previous results of McCleary which required the generalized continuum hypothesis and to be regular. |
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| Keywords: | 06F15 20E05 |
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