TL;DR
This paper explores the computability of F{46}lner sets in finitely generated amenable groups, providing explicit constructions and analyzing their properties in complex group structures.
Contribution
It introduces the notion of computability for F{46}lner sets, proves their computability in specific complex groups, and establishes bounds on the F{46}lner function in these contexts.
Findings
F{46}lner sets are computable in the Kharlampovich group.
Computability of F{46}lner sets extends to certain group extensions.
New upper bounds for the F{46}lner function in specific group extensions.
Abstract
We define the notion of computability of F{\o}lner 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 F{\o}lner sets. We also prove computability of F{\o}lner sets for a group that is extension of an amenable group with solvable word problem by a finitely generated group with computable F{\o}lner sets with subrecursive distortion function. Moreover we obtain some known and some new upper bounds for the F{\o}lner function in these particular extensions.
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Taxonomy
TopicsComputability, Logic, AI Algorithms