proposition: Lemma pcore_pgroup_id G : pi.-group G -> 'O_pi(G) = G.
proof: Proof. by move=> piG; apply/eqP; rewrite eqEsubset pcore_sub pcore_max. 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)