The fitting subgroup is the subgroup generated by all normal nilpotent subgroups of a group H, denoted F(H). 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 F^*(H) = F(H) E(H), where E(H) is the commuting product of all components of H and F is the fitting subgroup of H.
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