Representations of free lattice-ordered groups
Let \(\eta\) be any uncountable cardinal, \(G_ \eta\) be the free group and \(F_ \eta\) be the free lattice-ordered group of rank \(\eta\). The author shows that there exists a right ordering of \(G_ \eta\) on which the natural action of \(F_ \eta\) is both faithful and pathologically 2- transitive. Furthermore, he describes the structure of the root system of prime subgroups of \(F_ \eta\). The results obtained generalize analogous ones by \textit{S. H. McCleary} [Trans. Am. Math. Soc. 290, 81-100 (1985; Zbl 0546.06013)], where the generalized continuum hypothesis and regularity of \(\eta\) have been required.
scientific article; zbMATH DE number 549275