Some undecidability results for asynchronous transducers and the Brin-Thompson group $2V$
Some undecidability results for asynchronous transducers and the Brin-Thompson group $2V$
复制标题
异步传感器和 Brin-Thompson 组 $2V$ 的一些不可判定性结果
DOI：
10.1090/tran/6963
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发表时间：
2016
影响因子：
1.3
通讯作者：
Belk J
中科院分区：
文献类型：
--
作者：
Belk J
利用Kari和Ollinger的结果，证明了Brin-Thompson群元素的扭转问题是不可确定的。结果表明，不存在一种算法来确定Grigorchuk， Nekrashevich和sushchanski的有理群中的元素是否具有有限阶。对结构的修改给出了关于康托尔空间中元素作用的动力学的其他不可确定的结果。Arzhantseva, Lafont， and Minasyan在2012年证明了存在一个具有可解字问题和不可解扭转问题的有限呈现群。据我们所知，提供了这种群的第一个具体例子，并给出了R. Thompson型群的扩展家族的直接不可判定结果的例子。参考文献
Using a result of Kari and Ollinger, we prove that the torsion problem for elements of the Brin-Thompson groupis undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational groupof Grigorchuk, Nekrashevich, and Sushchanskiĭ has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements ofon Cantor space. Arzhantseva, Lafont, and Minasyan proved in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge,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. References