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Følner functions and the generic Word Problem for finitely generated amenable groups

We introduce and investigate different definitions of effective amenability, in terms of computability of Følner sets, Reiter functions, and Følner functions. As a consequence, we prove that recursively presented amenable groups have subrecursive Følner function, answering a question of Gromov; for...

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Bibliographic Details
Published in:Journal of algebra 2018-10, Vol.511, p.388-404
Main Author: Cavaleri, Matteo
Format: Article
Language:English
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Summary:We introduce and investigate different definitions of effective amenability, in terms of computability of Følner sets, Reiter functions, and Følner functions. As a consequence, we prove that recursively presented amenable groups have subrecursive Følner function, answering a question of Gromov; for the same class of groups we prove that solvability of the Equality Problem on a generic set (generic EP) is equivalent to solvability of the Word Problem on the whole group (WP), thus providing the first examples of finitely presented groups with unsolvable generic EP. In particular, we prove that for finitely presented groups, solvability of generic WP doesn't imply solvability of generic EP.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2018.06.017