We prove that the only finite factor representations of the Higman–Thompson groups and are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of the commutator subgroup of a Higman–Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.
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Artem Dudko, Konstantin Medynets, Finite factor representations of Higman–Thompson groups. Groups Geom. Dyn. 8 (2014), no. 2, pp. 375–389DOI 10.4171/GGD/230