Аннотация:We consider propositional normal unimodal pretransitive logics, i.e., logics with expressible `transitive' modality. There is a long-standing open problem about the finite model property (fmp) and decidability of pretransitive logics, in particular --for the logics K^m_n=K+ \Box^m p -> \Box^n p, n>m>1. A pretransitive logic L has the fmp or is decidable, only if these properties hold for the logic L.Sym, which is the extension of L with the symmetry axiom for `transitive' modality: like S5 can be embedded into S4, L.Sym can be embedded into L. We show that for all n>m>0, the logics K^m_n.Sym have the fmp. URL: http://math.hse.ru/data/2013/03/24/1307281546/paper73.pdf