Functional subgroups | Finite groups

Fitting subgroup

In mathematics, especially in the area of algebra known as group theory, the Fitting subgroup F of a finite group G, named after Hans Fitting, is the unique largest normal nilpotent subgroup 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 subgroup F*, which is generated by the Fitting subgroup and the components of G. For an arbitrary (not necessarily finite) group G, the Fitting subgroup is defined to be the subgroup generated by the nilpotent normal subgroups of G. For infinite groups, the Fitting subgroup is not always nilpotent. The remainder of this article deals exclusively with finite groups. (Wikipedia).

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From playlist Abstract algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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From playlist Abstract Algebra

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Normal subgroups

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From playlist Abstract algebra

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From playlist Abstract Algebra

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Related pages

Component (group theory) | Group extension | Chief series | Group of Lie type | Fitting length | Finite group | Simple group | Signalizer functor | Bender's method | Classification of finite simple groups | Characteristic subgroup | Mathematics | Fitting's theorem | Nilpotent group | Quasisimple group | Group theory | Cyclic group | Normal subgroup | Subnormal subgroup | Perfect group | Subgroup | Abstract algebra | Automorphism group | Solvable group | Local analysis