2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157848We prove that a one-dimensional foliation with generic singularities on a projective space, exhibiting a Lie group transverse structure in the complement of some codimension one algebraic subset is logarithmic, i.e., it is the intersection of codimension one foliations given by closed one-forms with simple poles. If there is only one singularity in a suitable affine space, then the foliation is induced by a linear diagonal vector field.Complex VariablesDynamical Systems37F75,text