  A nilpotent Cantor action is a minimal equicontinuous action $\Phi \colon
\Gamma \times \frak{X} \to \frak{X}$ on a Cantor set $\frak{X}$, where $\Gamma$
contains a finitely-generated nilpotent subgroup $\Gamma_0 \subset \Gamma$ of
finite index. In this note, we show that these actions are distinguished among
general Cantor actions: any effective action of a finitely generated group on a
Cantor space, which is continuously orbit equivalent to a nilpotent Cantor
action, must itself be a nilpotent Cantor action. As an application of this
result, we obtain new invariants of nilpotent Cantor actions under continuous
orbit equivalence.
