Section SplittingField.
Implicit Type gT : finGroupType.
Definition group_splitting_field gT (G : {group gT}) :=
forall n (rG : mx_representation F G n),
mx_irreducible rG -> mx_absolutely_irreducible rG.
Definition group_closure_field gT :=
forall G : {group gT}, group_splitting_field G.

(* Specifications: *)
Lemma quotient_splitting_field gT (G : {group gT}) (H : {set gT}) :
G \subset 'N(H) -> group_splitting_field G -> group_splitting_field (G / H).
Lemma coset_splitting_field gT (H : {set gT}) :
group_closure_field gT -> group_closure_field (coset_groupType H).