proposition: Lemma quotient_splitting_field gT (G : {group gT}) (H : {set gT}) : G \subset 'N(H) -> group_splitting_field G -> group_splitting_field (G / H).
proof: Proof. move=> nHG splitG n rGH irrGH. by rewrite -(morphim_mx_abs_irr _ nHG) splitG //; apply/morphim_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)