Finite complete rewriting systems for groups

Dekov, Deko V.

doi:10.1080/00927879708826106

Cited by 2 publications

(2 citation statements)

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“…In comparison, finite convergent rewriting systems have been found for all fundamental groups of Seifert fibered knot complements, namely the torus knot groups, by Dekov [11], and for fundamental groups of alternating knot complements, by Chouraqui [10]. In the case of a finite volume hyperbolic 3-manifold M , the fundamental group π 1 (M ) is hyperbolic relative to the collection of fundamental groups of its torus boundary components by a result of Farb [13], and so by closure of the class of (prefix-closed) biautomatic groups with respect to relative hyperbolicity (shown by Rebbecchi in [27]; see also [1]), the group π 1 (M ) is biautomatic.…”

Section: Introductionmentioning

confidence: 99%

Geometry of the word problem for 3-manifold groups

2018

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We provide an algorithm to solve the word problem in all fundamental groups of closed 3-manifolds; in particular, we show that these groups are autostackable. This provides a common framework for a solution to the word problem in any closed 3-manifold group using finite state automata. We also introduce the notion of a group which is autostackable respecting a subgroup, and show that a fundamental group of a graph of groups whose vertex groups are autostackable respecting any edge group is autostackable. A group that is strongly coset automatic over an autostackable subgroup, using a prefix-closed transversal, is also shown to be autostackable respecting that subgroup. Building on work by Antolin and Ciobanu, we show that a finitely generated group that is hyperbolic relative to a collection of abelian subgroups is also strongly coset automatic relative to each subgroup in the collection. Finally, we show that fundamental groups of compact geometric 3-manifolds, with boundary consisting of (finitely many) incompressible torus components, are autostackable respecting any choice of peripheral subgroup.Comment: 32 pages, 1 figur

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Section: Introductionmentioning

confidence: 99%

Geometry of the word problem for 3-manifold groups

2018

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“…(See [10] or [22] for more information about rewriting systems for groups and their applications.) Examples of groups with finite complete rewriting systems include finite groups, surface groups [19], constructible solvable groups [12], tame prime alternating [6] and torus [9] knot groups, and Artin groups of finite type [15]; this class is closed under group extensions [12,15] and graph products [13]. Theorem 4.1.…”

Section: Introductionmentioning

confidence: 99%

A uniform model for almost convexity and rewriting systems

Brittenham

Hermiller

2015

Journal of Group Theory

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We introduce a topological property for finitely generated groups, called stackable, that implies the existence of an inductive procedure for constructing van Kampen diagrams with respect to a particular finite presentation. We also define algorithmically stackable groups, for which this procedure is an algorithm. This property gives a common model for algorithms arising from both rewriting systems and almost convexity for groups.

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Finite complete rewriting systems for groups

Cited by 2 publications

References 8 publications

Geometry of the word problem for 3-manifold groups

Geometry of the word problem for 3-manifold groups

A uniform model for almost convexity and rewriting systems

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