2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139738We give an explicit formula for the subalgebra zeta function of a general 3-dimensional Lie algebra over the p-adic integers $\mathbb{Z}_p$. To this end, we associate to such a Lie algebra a ternary quadratic form over $\mathbb{Z}_p$. The formula for the zeta function is given in terms of Igusa's local zeta function associated to this form.20 pagesGroup Theory20E07; 11S40; 11E20text