2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218596Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function ξon Wiener space into G via the stochastic version of Cartan's rolling map. It is shown here that, for any smooth function f with compact support, f(ξ) is Malliavin differentiable to all orders and these derivatives belong to L^p(μ) for all p>1, where μis Wiener measure.22 pages, 0 figures; final version with addition of example and significant reorganization, to appear in Infinite Dimensional Analysis and Quantum ProbabilityProbability60H07, 58J65 (Primary); 22E99 (Secondary)text