# Generalized Fitting subgroup

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*This article is about a term related to the Classification of finite simple groups*

## 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 components).

### Definition with symbols

Let be a group. The generalized Fitting subgroup of , denoted as , is defined as the product , where is the Fitting subgroup and is the layer.

## Relation with other subgroup-defining functions

### Smaller subgroup-defining functions

## Subgroup properties satisfied

- Characteristic subgroup
- Self-centralizing subgroup: The generalized Fitting subgroup of any group is self-centralizing.
`For full proof, refer: generalized Fitting is self-centralizing`