proposition: Lemma cpair_center_id : 'Z(CH) = 'Z(CK).
proof: Proof. rewrite -!injm_center // -gzZ -morphim_comp; apply: eq_in_morphim eq_cpairZ. by rewrite !(setIidPr _) // -sub_morphim_pre. 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)