Discretely ordered groups

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dc.creatorLinnell, Peter A.
dc.creatorRhemtulla, Akbar H.
dc.creatorRolfsen, Dale P. O.
dc.date2008-08-20
dc.date2009-05-05
dc.date.accessioned2026-07-07T13:11:08Z
dc.date.available2026-07-07T13:11:08Z
dc.descriptionWe consider group orders and right-orders which are discrete, meaning there is a least element which is greater than the identity. We note that free groups cannot be given discrete orders, although they do have right-orders which are discrete. More generally, we give necessary and sufficient conditions that a given orderable group can be endowed with a discrete order. In particular, every orderable group G embeds in a discretely orderable group. We also consider conditions on right-orderable groups to be discretely right-orderable. Finally, we discuss a number of illustrative examples involving discrete orderability, including the Artin braid groups and Bergman's non-locally-indicable right orderable groups.
dc.description9 pages, minor changes, to appear in Algebra and Number theory
dc.identifierhttps://arxiv.org/abs/0808.2686
dc.identifierhttp://arxiv.org/abs/0808.2686
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/229196
dc.subjectGroup Theory
dc.subject20F60 (Primary) 06F15, 20F36 (Secondary)
dc.titleDiscretely ordered groups
dc.typetext

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