The number of non-solutions to an equation in a group and non-topologizable torsion-free groups

Simple item page
dc.creatorKlyachko, Anton A.
dc.creatorTrofimov, Anton V.
dc.date2004-11-07
dc.date2004-11-10
dc.date.accessioned2026-07-07T06:26:16Z
dc.date.available2026-07-07T06:26:16Z
dc.descriptionIt is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions to this equation. A countable torsion-free non-topologizable group is constructed.
dc.description5 pages; minor changes in the introduction and references
dc.identifierhttps://arxiv.org/abs/math/0411156
dc.identifierhttp://arxiv.org/abs/math/0411156
dc.identifierJournal of Group Theory, Volume: 8 (2005), Issue: 6 Pages: 747-754 (under the title "The number of non-solutions of an equation in a group")
dc.identifierdoi:10.1515/jgth.2005.8.6.747
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97060
dc.subjectGroup Theory
dc.subjectGeneral Topology
dc.subject20F05, 20F06, 22A05, 54H11
dc.titleThe number of non-solutions to an equation in a group and non-topologizable torsion-free groups
dc.typetext

Files

Collections

arXiv