Fitting series

Definition
A Fitting series or nilpotent series for a solvable group is a subnormal series (of finite length?) where each quotient between successive groups is a nilpotent group.

The fastest possible descending Fitting series for a finite solvable group is the lower Fitting series, defined by iterating the nilpotent residual. For infinite solvable groups, there may or may not be a fastest possible descending Fitting series.

The fastest possible ascending Fitting series for a finite solvable group is the upper Fitting series.