  This work provides a characterization of the regularity of noncharacteristic
intrinsic minimal graphs for a class of vector fields that includes non
nilpotent Lie algebras as the one given by Euclidean motions of the plane. The
main result extends a previous one on the Heisenberg group, using similar
techniques to deal with nonlinearities. This wider setting provides a better
understanding of geometric constraints, together with an extension of the
potentialities of specific tools as the lifting-freezing procedure and
interpolation inequalities. As a consequence of the regularity, a foliation
result for minimal graphs is obtained.
