proposition: Lemma external_action_im_coprime : coprime #|G'| #|A'|.
proof: Proof. by rewrite !card_injm. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq div choice) mathcomp(fintype finset prime fingroup morphism) mathcomp(automorphism quotient action gproduct gfunctor) mathcomp(commutator center pgroup finmodule nilpotent) mathcomp(sylow abelian maximal)