Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V
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.
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
Publication
Transactions of the American Mathematical Society
Status
Peer reviewed
ISSN
0002-9947Type
Journal article
Description
Funding: partial support by UK EPSRC grant EP/H011978/1 (CB).Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.