proposition: Lemma cprod_center_id G : G \* 'Z(G) = G.
proof: Proof. by rewrite cprodE ?subsetIr // mulGSid ?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)