Fitting subgroup

Summary

The Fitting subgroup $F(G)$ of a finite group $G$ is the largest nilpotent normal subgroup of $G$. It exists because the product of two nilpotent normal subgroups is again nilpotent, a theorem of Hans Fitting. In a solvable group $G$, the Fitting subgroup contains its own centraliser, so it controls much of the structure of $G$. It is a basic tool in the theory of finite solvable groups.