Fitting Subgroup

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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Aschbacher, M. Finite Group Theory, 2nd ed. Cambridge, England: Cambridge University Press, 2000.

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Fitting Subgroup

Cite this as:

Weisstein, Eric W. "Fitting Subgroup." From MathWorld--A Wolfram Web Resource.

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