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dc.contributor.authorBennett, Daniel
dc.contributor.authorBleak, Collin
dc.identifier.citationBennett , D & Bleak , C 2016 , ' A dynamical definition of f.g. virtually free groups ' , International Journal of Algebra and Computation , vol. 26 , no. 1 , pp. 105-121 .
dc.identifier.otherORCID: /0000-0001-5790-1940/work/73701277
dc.description.abstractWe show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson's group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0,1}ω. There are also connections with formal language theory, as the class of groups with context-free word problem is also the class of finitely generated virtually free groups, while R. Thompson's group V is a candidate as a universal coCF group by Lehnert's conjecture, corresponding to the class of groups with context free co-word problem (as introduced by Holt, Rees, Röver, and Thomas). Our main results answers a question of Berns-Zieze, Fry, Gillings, Hoganson, and Matthews, and separately of Bleak and Salazar-Días, and fits into the larger exploration of the class of coCF groups as it shows that all four of the known properties of the class of coCF groups hold for the set of finitely generation subgroups of V .
dc.relation.ispartofInternational Journal of Algebra and Computationen
dc.subjectCoCF groupsen
dc.subjectThompson Groupsen
dc.subjectLehnert's Conjectureen
dc.subjectGroup actionsen
dc.subjectGeometric actionsen
dc.subjectQA Mathematicsen
dc.titleA dynamical definition of f.g. virtually free groupsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.contributor.institutionUniversity of St Andrews. Centre for Interdisciplinary Research in Computational Algebraen
dc.description.statusPeer revieweden

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