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Exact descriptions of F{\o}lner functions and sets on wreath products and Baumslag-Solitar groups

Bogdan Stankov
arXiv: Group Theory
Nov 2021
摘要
We calculate the exact values of the F{\o}lner function of the lamplighter group for the standard generating set, as well as the F{\o}lner sets that give rise to it. F{\o}lner functions encode the isoperimetric properties of amenable groups and have previously been studied up to asymptotic equivalence (that is to say, independently of the choice of finite generating set). What is more, we prove an isoperimetric result concerning the edge boundary on the Baumslag-Solitar group $BS(1,2)$ for the standard generating set.
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