2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66932Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these groups, we find the dimension of the spaces of $G$-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding $G$-invariant pencils of surfaces in $\mathbb{P}_3$ which we started in math. AG/0106080. It turns out that we have five more pencils, two of them containing surfaces with nodes.29 pages, 1 figureAlgebraic Geometrytext