Generalized Fitting subgroup

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 $$G$$ be a group. The generalized Fitting subgroup of $$G$$, denoted as $$F^*(G)$$, is defined as the product $$F(G)E(G)$$, where $$F(G)$$ is the Fitting subgroup and $$E(G)$$ is the layer.

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.