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A dynamical definition of f.g. virtually free groups
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dc.contributor.author | Bennett, Daniel | |
dc.contributor.author | Bleak, Collin | |
dc.date.accessioned | 2017-01-23T00:32:18Z | |
dc.date.available | 2017-01-23T00:32:18Z | |
dc.date.issued | 2016-02 | |
dc.identifier.citation | Bennett , 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 . https://doi.org/10.1142/S0218196716500053 | en |
dc.identifier.issn | 0218-1967 | |
dc.identifier.other | PURE: 231627251 | |
dc.identifier.other | PURE UUID: 43a099ed-e2d3-4b70-afa1-b70e757a7f31 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1510.02638v1 | |
dc.identifier.other | Scopus: 84959223469 | |
dc.identifier.other | WOS: 000371092100005 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/73701277 | |
dc.identifier.uri | https://hdl.handle.net/10023/10148 | |
dc.description.abstract | We 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.format.extent | 17 | |
dc.language.iso | eng | |
dc.relation.ispartof | International Journal of Algebra and Computation | en |
dc.rights | © 2016, World Scientific Publishing Company. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.worldscientific.com / https://dx.doi.org/10.1142/S0218196716500053 | en |
dc.subject | CoCF groups | en |
dc.subject | Thompson Groups | en |
dc.subject | Lehnert's Conjecture | en |
dc.subject | Group actions | en |
dc.subject | Geometric actions | en |
dc.subject | QA Mathematics | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | A dynamical definition of f.g. virtually free groups | en |
dc.type | Journal article | en |
dc.description.version | Postprint | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | https://doi.org/10.1142/S0218196716500053 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2017-01-22 |
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