proposition: Lemma Fitting_eq_pcore p G : 'O_p^'(G) = 1 -> 'F(G) = 'O_p(G).
proof: Proof. move=> p'G1; have /dprodP[_ /= <- _ _] := nilpotent_pcoreC p (Fitting_nil G). by rewrite p_core_Fitting ['O_p^'(_)](trivgP _) ?mulg1 // -p'G1 pcore_Fitting. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(div fintype finfun bigop finset prime binomial) mathcomp(fingroup morphism perm automorphism quotient) mathcomp(action commutator gproduct gfunctor ssralg) mathcomp(countalg finalg zmodp cyclic pgroup center gseries) mathcomp(nilpotent sylow abelian finmodule)