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{{subgroup-defining function}}

{{stdnonbasicdef}}

{{cfsg}}

==Definition==

===Symbol-free definition===

The '''generalized Fitting subgroup''' of a group is defined as the product of its [[Fitting subgroup]] with its [[layer]] (the layer here is the commuting product of all the [[component]]s).

===Definition with symbols===

Let <math>G</math> be a [[group]]. The generalized Fitting subgroup of <math>G</math>, denoted as <math>F^*(G)</math>, is defined as the product <math>F(G)E(G)</math>, where <math>F(G)</math> is the [[Fitting subgroup]] and <math>E(G)</math> is the [[layer]].

==Relation with other subgroup-defining functions==

===Smaller subgroup-defining functions===

* [[Layer]]
* [[Fitting subgroup]]

==Subgroup properties satisfied==

* [[Characteristic subgroup]]
* [[Self-centralizing subgroup]]: The generalized Fitting subgroup of any group is self-centralizing. {{proofat|[[generalized Fitting is self-centralizing]]}}

Generalized Fitting subgroup - Revision history

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