Fitting length

The concept is named after Hans Fitting, due to his investigations of nilpotent normal subgroups.

These correspond to the center and the commutator subgroup (for upper and lower central series, respectively).

It is an ascending nilpotent series, at each step taking the maximal possible subgroup.

It is a descending nilpotent series, at each step taking the minimal possible subgroup.

The successive quotients are abelian, showing the equivalence between being solvable and having a Fitting series.

Combining the lower Fitting series and lower central series on a solvable group yields a series with coarse and fine divisions, like the coarse and fine marks on a ruler.