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Algorithms and topology of Cayley graphs for groups
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Brittenham, Mark, Hermiller, Susan and Holt, Derek F. (2014) Algorithms and topology of Cayley graphs for groups. Journal of Algebra, Volume 415 . pp. 112-136. doi:10.1016/j.jalgebra.2014.06.001 ISSN 0021-8693.
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Official URL: http://dx.doi.org/10.1016/j.jalgebra.2014.06.001
Abstract
Autostackability for finitely generated groups is defined via a topological property of the associated Cayley graph which can be encoded in a finite state automaton. Autostackable groups have solvable word problem and an effective inductive procedure for constructing van Kampen diagrams with respect to a canonical finite presentation. A comparison with automatic groups is given. Another characterization of autostackability is given in terms of prefix-rewriting systems. Every group which admits a finite complete rewriting system or an asynchronously automatic structure with respect to a prefix-closed set of normal forms is also autostackable. As a consequence, the fundamental group of every closed 3-manifold with any of the eight possible uniform geometries is autostackable.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal of Algebra | ||||||||
Publisher: | Academic Press Inc Elsevier Science | ||||||||
ISSN: | 0021-8693 | ||||||||
Official Date: | October 2014 | ||||||||
Dates: |
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Volume: | Volume 415 | ||||||||
Page Range: | pp. 112-136 | ||||||||
DOI: | 10.1016/j.jalgebra.2014.06.001 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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