Computability of Flner sets
Abstract
We define the notion of computability of Flner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has computable Flner sets. We also prove computability of Flner sets for a group that is extension of an amenable group with solvable word problem by a finitely generated group with computable Flner sets with subrecursive distortion function. Moreover we obtain some known and some new upper bounds for the Flner function in these particular extensions.
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