Notation for subgroup-defining functions

For convenience of notation, $$G$$ here denotes the group on which we are computing the subgroup-defining function.

Subgroup-defining functions

 * $$Soc(G)$$ denotes the socle of $$G$$
 * $$W(G)$$ denotes the Wielandt subgroup of $$G$$
 * $$O(G)$$ denotes the Brauer core of $$G$$
 * $$E(G)$$ denotes the layer of $$G$$
 * $$F^*(G)$$ denotes the generalized Fitting subgroup of $$G$$
 * $$L(G)$$ denotes the 2-layer of $$G$$