Finitely presented residually free groups
| Autor: | Bridson, Martin R., Howie, James, Miller III, Charles F., Short, Hamish |
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| Rok vydání: | 2008 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We 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. Comment: 38 pages |
| Databáze: | arXiv |
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