Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V
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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.
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
Transactions of the American Mathematical Society
© Copyright 2016 American Mathematical Society. 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 https://doi.org/10.1090/tran/6963
DescriptionFunding: partial support by UK EPSRC grant EP/H011978/1 (CB).
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