2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141742Given a finite group $H$ and a free group $F_n$, we prove that the wreath product $H\wr F_n$ admits a metrically proper, isometric action on a Hilbert space.6 pages. The part on Hilbert space compression from the first version of this paper, will be incorporated into a more elaborate paper on the subjectGroup Theory20E22 (primary); 20F65 (Secondary)text