proposition: Lemma sub_center_normal H G : H \subset 'Z(G) -> H <| G.
proof: Proof. by rewrite subsetI centsC /normal => /andP[-> /cents_norm]. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div) mathcomp(fintype bigop finset fingroup morphism perm) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(cyclic)