PENTAGONAL TRANSFORMATIONS

We prove that every bimeasurable transformation v : X x X --> X x X, w here X is a measured space satisfying the pentagon identity v(23) o v( 13) o v(12) = v(12) o v(23) (and sufficiently regular) comes from a ma tched pair of locally compact groups (cf. [5], [8], [6], [2]), i.e. a locally compact group G and two closed subgroups, G(1) and G(2) such t hat the map (g(1),g(2)) bar right arrow g(1)g(2) is a homeomorphism fr om G(1) x G(2) onto a dense open subset of G. (C) Academie des Science s/Elsevier, Paris.