Topological full groups are locally embeddable into finite groups

Details Topological full groups are locally embeddable into finite groups Topological full groups are locally embeddable into finite groups

2011-05-04

arxiv.org/abs/1105.0719v3

Mathematics

Group Theory

Scientific paper

This note is a correction of our preprint "On simple finitely generated amenable groups". We prove that the topological full group $[[T]]$ of any Cantor minimal system $(X,T)$ is locally embeddable into finite groups (an LEF group). The LEF property allows us to get a new proof of Matui's result that the commutator subgroup $[[T]]'$ cannot be finitely presented. The LEF property also implies that the group $[[T]]$ is sofic.

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