  We study several notions of null sets on infinite-dimensional Carnot groups.
We prove that a set is Aronszajn null if and only if it is null with respect to
measures that are convolutions of absolutely continuous (CAC) measures on
Carnot subgroups. The CAC measures are the non-abelian analogue of cube
measures. In the case of infinite-dimensional Heisenberg-like groups we also
show that being null in the previous senses is equivalent to being null for all
heat kernel measures. Additionally, we show that infinite-dimensional Carnot
groups that have locally compact commutator subgroups have the structure of
Banach manifolds. There are a number of open questions included as well.

Metric Geometry;Classical Analysis and ODEs