proposition: Lemma center_cprod A B G : A \* B = G -> 'Z(A) \* 'Z(B) = 'Z(G).
proof: Proof. case/cprodP => [[H K -> ->] <- cHK]. rewrite cprodE ?center_prod //= subIset ?(subset_trans cHK) //. by rewrite centS ?center_sub. 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)