proposition: Lemma der1_sub_rker : group_splitting_field G -> mx_irreducible rG -> (G^`(1) \subset rker rG)%g = (n == 1)%N.
proof: Proof. move=> splitG irrG; apply/idP/idP; last by move/eqP; apply: rker_linear. move/sub_der1_abelian; move/(abelian_abs_irr (kquo_repr rG))=> <-. by apply: (quotient_splitting_field (rker_norm _) splitG); apply/quo_mx_irr. 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)