2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102315For a wide class of groups including polycyclic and finitely generated polynomial growth groups it is proved that the Reidemeister number of an automorphism f is equal to the number of finite-dimensional fixed points of the induced map f^ on the unitary dual, if one of these numbers is finite. This theorem is a natural generalization of the classical Burnside-Frobenius theorem to infinite groups. This theorem also has important consequences in topological dynamics and in some sense is a reply to a remark of J.-P. Serre. The main technical results proved in the paper yield a tool for a further progress.17 pages, no figures, v2: some small improvements using referee's suggestionsGroup TheoryNumber TheoryOperator AlgebrasRepresentation Theory20Cxx; 20E45; 22D10; 22D25; 43A30; 46Lxx; 37C25; 54H25text