proposition: Lemma pcore_psubgroup G : pi.-subgroup(G) 'O_pi(G).
proof: Proof. have [M maxM _]: {M | [max M | pi.-subgroup(G) M] & 1%G \subset M}. by apply: maxgroup_exists; rewrite /psubgroup sub1G pgroup1. have sOM: 'O_pi(G) \subset M by apply: bigcap_inf. have /andP[piM sMG] := maxgroupp maxM. by rewrite /psubgroup (pgroupS sOM) // (subset_trans sOM). 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)