Margulis, G. A. Free totally discontinuous groups of affine transformations. (English. Russian original) Zbl 0578.57012 Sov. Math., Dokl. 28, 435-439 (1983); translation from Dokl. Akad. Nauk SSSR 272, 785-788 (1983). The Milnor conjecture (the fundamental group of any complete affine variety is almost polycyclic) may be formulated in the following equivalent form: any subgroup of the affine transformation group A(n) which acts totally discontinuously on \({\mathbb{R}}^ n\) is almost polycyclic (i.e. contains a polycyclic subgroup of finite index). In this note it is proved that for \(n=3\) the answer to this conjecture is negative. Reviewer: A.Neagu Cited in 11 ReviewsCited in 18 Documents MSC: 57S30 Discontinuous groups of transformations 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) 22E40 Discrete subgroups of Lie groups Keywords:semidirect product; totally discontinuous actions on \({\mathbb{R}}^ n\); Milnor conjecture; affine variety; affine transformation group; polycyclic subgroup PDFBibTeX XMLCite \textit{G. A. Margulis}, Sov. Math., Dokl. 28, 435--439 (1983; Zbl 0578.57012); translation from Dokl. Akad. Nauk SSSR 272, 785--788 (1983)