On decidability of amenability in computable groups

Computable paradoxical decompositions

“…• Are there natural examples with non-computable W BT ? In [8] (see also [7]) we give an example of a finitely presented group, say H nA , with decidable word problem such that detection of all finite subsets of H nA which generate amenable subgroups, is not decidable. Applying Proposition 4.5 we see that the set W BT is not computable in this group.…”

“…Applying Proposition 4.5 we see that the set W BT is not computable in this group. In [8] we used slightly involved methods of computability theory. It can be also derived from [8] and [7] that when a computable group G is fully residually free [11], the corresponding set W BT is computable.…”