Abstract.It is easy to pose questions about the free lattice-ordered group Fv of rank tj > 1 whose answers2 are "obvious", but difficult to verify. Question 1 was answered recently by Medvedev, and both 1 and 2 by Arora and McCleary, using Conrad's representation of Fv via right orderings of the free group Gv. Here we answer all four questions by using a completely different tool: The (faithful) representation of Fv as an o-2-transitive /-permutation group which is pathological (has no nonidentity element of bounded support). This representation was established by Glass for most infinite tj, and is here extended to all q > 1. Curiously, the existence of a transitive representation for Fv implies (by a result of Kopytov) that in the Conrad representation there is some right ordering of Gv which suffices all by itself to give a faithful representation of Fv. For finite tj, we find that every transitive representation of Fv can be made from a pathologically o-2-transitive representation by blowing up the points to o-blocks; and every pathologically o-2-transitive representation of Fv can be extended to a pathologically o-2-transitive representation of F .

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