On decidability of amenability in computable groups

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Archive for Mathematical Logic 61 (7):891-902 (2022)
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Abstract

The main result of the paper states that there is a finitely presented group _G_ with decidable word problem where detection of finite subsets of _G_ which generate amenable subgroups is not decidable.

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10.1007/s00153-022-00819-5

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References found in this work

Hyperlinear and sofic groups: a brief guide.Vladimir G. Pestov - 2008 - Bulletin of Symbolic Logic 14 (4):449-480.
Possible degrees in recursive copies II.C. J. Ash & J. F. Knight - 1997 - Annals of Pure and Applied Logic 87 (2):151-165.
Computability, orders, and solvable groups.Arman Darbinyan - 2020 - Journal of Symbolic Logic 85 (4):1588-1598.
An Embedding Theorem for Finitely Generated Groups.C. R. J. Clapham - 1970 - Journal of Symbolic Logic 35 (2):340-341.

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