proposition: Lemma pcore_max G H : pi.-group H -> H <| G -> H \subset 'O_pi(G).
proof: Proof. move=> piH nHG; apply/bigcapsP=> M maxM. exact: normal_sub_max_pgroup piH nHG. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset prime fingroup morphism) mathcomp(gfunctor automorphism quotient action gproduct) mathcomp(cyclic)