In mathematics, especially in the area of algebra known as group theory, the Fitting subgroupF of a finitegroupG, named after Hans Fitting, is the unique largest normalnilpotentsubgroup of G. Intuitively, it represents the smallest subgroup which "controls" the structure of G when G is solvable. When G is not solvable, a similar role is played by the generalized Fitting subgroupF*, which is generated by the Fitting subgroup and the components of G.