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Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V
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dc.contributor.author | Belk, James | |
dc.contributor.author | Bleak, Collin | |
dc.date.accessioned | 2016-03-29T14:30:05Z | |
dc.date.available | 2016-03-29T14:30:05Z | |
dc.date.issued | 2017-05 | |
dc.identifier | 231626907 | |
dc.identifier | 50911412-001d-4b6a-b482-6460b959e930 | |
dc.identifier | 85012076965 | |
dc.identifier | 000398030400005 | |
dc.identifier.citation | Belk , J & Bleak , C 2017 , ' Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V ' , Transactions of the American Mathematical Society , vol. 369 , no. 5 , pp. 3157-3172 . https://doi.org/10.1090/tran/6963 | en |
dc.identifier.issn | 0002-9947 | |
dc.identifier.other | ArXiv: http://arxiv.org/abs/1405.0982v1 | |
dc.identifier.other | ORCID: /0000-0001-5790-1940/work/73701282 | |
dc.identifier.uri | https://hdl.handle.net/10023/8508 | |
dc.description | Funding: partial support by UK EPSRC grant EP/H011978/1 (CB). | en |
dc.description.abstract | Using a result of Kari and Ollinger, we prove that the torsion problem for elements of the Brin-Thompson group 2V is undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational group R of Grigorchuk, Nekrashevich, and Sushchanskiĭ has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements of 2V on Cantor space. Arzhantseva, Lafont, and Minasyanin proved in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge, 2V furnishes the first concrete example of such a group and gives an example of a direct undecidability result in the extended family of R. Thompson type groups. | |
dc.format.extent | 16 | |
dc.format.extent | 374380 | |
dc.language.iso | eng | |
dc.relation.ispartof | Transactions of the American Mathematical Society | en |
dc.subject | Undecidable torsion problem | en |
dc.subject | Brin-Thompson groups | en |
dc.subject | Rational group | en |
dc.subject | Transducer | en |
dc.subject | Reversible Turing machine | en |
dc.subject | QA75 Electronic computers. Computer science | en |
dc.subject | T-NDAS | en |
dc.subject | BDC | en |
dc.subject | R2C | en |
dc.subject.lcc | QA75 | en |
dc.title | Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V | en |
dc.type | Journal article | en |
dc.contributor.sponsor | EPSRC | 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 | 10.1090/tran/6963 | |
dc.description.status | Peer reviewed | en |
dc.identifier.grantnumber | EP/H011978/1 | en |
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