proposition: Lemma subcent1_cycle_normal x G : x \in G -> <[x]> <| 'C_G[x].
proof: Proof. by move=> Gx; rewrite /normal subcent1_cycle_norm subcent1_cycle_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)