Primitives of volume forms in Carnot groups

In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\mathrm{\parallel }F\mathrm{\parallel }\mathrm{\_}{L}^2(B)\le C\mathrm{\parallel }f\mathrm{\parallel }\mathrm{\_}{L}^2(B)\mathrm{.}$$In this Note we prove a similar result in any Carnot group $\mathbb{G}$ for a vanishing average $f\in L^p$, $1\le p<Q$, where $Q$ is the so-called homogeneous dimension of $\mathbb{G}$.