  In studying nilpotent groups, the lower central series and other variations
can be used to construct an associated $\mathbb{Z}^+$-graded Lie ring, which is
a powerful method to inspect a group. Indeed, the process can be generalized
substantially by introducing $\mathbb{N}^d$-graded Lie rings. We compute the
adjoint refinements of the lower central series of the unipotent subgroups of
the classical Chevalley groups over the field $\mathbb{Z}/p\mathbb{Z}$ of rank
$d$. We prove that, for all the classical types, this characteristic filter is
a series of length $\Theta(d^2)$ with nearly all factors having $p$-bounded
order.

Group Theory