  This paper contributes to the generalization of Rademacher's
differentiability result for Lipschitz functions when the domain is infinite
dimensional and has nonabelian group structure. We introduce the notion of
metric scalable groups which are our infinite-dimensional analogues of Carnot
groups. The groups in which we will mostly be interested are the ones that
admit a dense increasing sequence of (finite-dimensional) Carnot subgroups. In
fact, in each of these spaces we show that every Lipschitz function has a point
of G\^{a}teaux differentiability. We provide examples and criteria for when
such Carnot subgroups exist. The proof of the main theorem follows the work of
Aronszajn and Pansu.
