Finitely presented residually free groups

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dc.creatorBridson, Martin R.
dc.creatorHowie, James
dc.creatorMiller III, Charles F.
dc.creatorShort, Hamish
dc.date2008-09-22
dc.date.accessioned2026-07-07T10:04:25Z
dc.date.available2026-07-07T10:04:25Z
dc.descriptionWe establish a general criterion for the finite presentability of subdirect products of groups and use this to characterize finitely presented residually free groups. We prove that, for all $n\in\mathbb{N}$, a residually free group is of type ${\rm{FP}}_n$ if and only if it is of type ${\rm{F}}_n$. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups that are neither ${\rm{FP}}_\infty$ nor of Stallings-Bieri type. The template for these examples leads to a more constructive characterization of finitely presented residually free groups up to commensurability. We show that the class of finitely presented residually free groups is recursively enumerable and present a reduction of the isomorphism problem. A new algorithm is described which, given a finite presentation of a residually free group, constructs a canonical embedding into a direct product of finitely many limit groups. The (multiple) conjugacy and membership problems for finitely presented subgroups of residually free groups are solved.
dc.description38 pages
dc.identifierhttps://arxiv.org/abs/0809.3704
dc.identifierhttp://arxiv.org/abs/0809.3704
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169671
dc.subjectGroup Theory
dc.subject20F65
dc.titleFinitely presented residually free groups
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