Groupprops, The Group Properties Wiki (pre-alpha)

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From Groupprops

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).