End Frattini4.
Section Fitting.
Variable gT : finGroupType.
Implicit Types (p : nat) (G H : {group gT}).

(* Specifications: *)
Lemma Fitting_normal G : 'F(G) <| G.
Lemma Fitting_sub G : 'F(G) \subset G.
Lemma Fitting_max G H : H <| G -> nilpotent H -> H \subset 'F(G).
Lemma pcore_Fitting pi G : 'O_pi('F(G)) \subset 'O_pi(G).
Lemma nilpotent_Fitting G : nilpotent G -> 'F(G) = G.
Lemma Fitting_eq_pcore p G : 'O_p^'(G) = 1 -> 'F(G) = 'O_p(G).
Lemma FittingEgen G :
'F(G) = <<\bigcup_(p < #|G|.+1 | (p : nat) \in \pi(G)) 'O_p(G)>>.