proposition: Fact rcenter_group_set : group_set rcenter.
proof: Proof. apply/group_setP; split=> [|x y]. by rewrite inE group1 repr_mx1 scalar_mx_is_scalar. move=> /setIdP[Gx /is_scalar_mxP[a defx]] /setIdP[Gy /is_scalar_mxP[b defy]]. by rewrite !inE groupM ?repr_mxM // defx defy -scalar_mxM ?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)