2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142637We construct a compact example of 7- dimensional manifold endowed with a weakly integrable generalized G_2-structure with respect to a closed and non trivial 3-form. Moreover, we investigate which type of SU(3)-structures on a 6-dimensional manifold N give rise to a strongly integrable generalized G_2-structure with respect to a non trivial 3-form on the product $N \times S^1$.Removed a section and added another one. Final version will appear in Internat. J. MathDifferential Geometry53C10; 53C25; 83E50text