proposition: Lemma subcent1_id x G : x \in G -> x \in 'C_G[x].
proof: Proof. by move=> Gx; rewrite inE Gx; apply/cent1P. 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)