proposition: Lemma rcenter_normal : rcenter <| G.
proof: Proof. rewrite /normal /rcenter {1}setIdE subsetIl; apply/subsetP=> x Gx /[1!inE]. apply/subsetP=> _ /imsetP[y /setIdP[Gy /is_scalar_mxP[c rGy]] ->]. rewrite inE !repr_mxM ?groupM ?groupV //= mulmxA rGy scalar_mxC repr_mxKV //. exact: scalar_mx_is_scalar. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)