proposition: Lemma cfker_center_normal phi : cfker phi <| 'Z(phi)%CF.
proof: Proof. apply: normalS (cfcenter_sub phi) (cfker_normal phi). rewrite /= /cfcenter; case: ifP => // Hphi; rewrite cfkerEchar //. apply/subsetP=> x /[!inE] /andP[-> /eqP->] /=. by rewrite ger0_norm ?char1_ge0. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)