Abstract
The definition of the free lattice-ordered group F η of a given rank η is analogous to that of the free group G η. Yet there are many questions which have the same “obvious” answers in both contexts, and for which the answers are very easy to confirm for free groups but not at all easy for free l-groups. We assume η > 1. Some questions:
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1.
Does F η have solvable word problem?
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2.
What is the center of F η?
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3.
What is the centralizer of a free generator x?
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4.
Is F η directly indecomposable?
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5.
Does F η have a basic element?
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6.
Is F η completely distributive?
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© 1989 Kluwer Academic Publishers
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McCleary, S.H. (1989). Free Lattice-Ordered Groups. In: Glass, A.M.W., Holland, W.C. (eds) Lattice-Ordered Groups. Mathematics and Its Applications, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2283-9_10
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DOI: https://doi.org/10.1007/978-94-009-2283-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7524-4
Online ISBN: 978-94-009-2283-9
eBook Packages: Springer Book Archive