The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group 
, denoted 
.
In the case of a finite group, the subgroup generated will itself be a normal nilpotent subgroup, and hence the unique largest normal nilpotent subgroup.
The generalized fitting subgroup is defined by 
, where 
is the commuting product of all components of 
and 
is the fitting subgroup of 
.
