Fitting length

This article defines an arithmetic function on a restricted class of groups, namely: solvable groups

Definition

Symbol-free definition

Given a solvable group, we can define its Fitting length as follows: It is the length of the Fitting series of the group. The Fitting series is an ascending series defined via quotient-iteration of the Fitting subgroup. That is, we define $F_{i}(G)$ so that $F_{i}(G)/F_{i-1}$ is the Fitting subgroup of $G/F_{i-1}(G)$.