proposition: Lemma cpair1g_center : cpair1g @* 'Z(K) = 'Z(C).
proof: Proof. case/cprodP: (center_cprod im_cpair_cprod) => _ <- _. by rewrite injm_center // -setI_im_cpair mulSGid //= setIC setIS 1?centsC. 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)