Section Transfer.
Variables (gT aT : finGroupType) (G H : {group gT}).
Variable alpha : {morphism H >-> aT}.
Hypotheses (sHG : H \subset G) (abelA : abelian (alpha @* H)).
Local Notation HG := (rcosets (gval H) (gval G)).
Fact transfer_morph_subproof : H \subset alpha @*^-1 (alpha @* H).
Canonical transfer_morphism := Morphism transferM.

(* Specifications: *)
(* This is Aschbacher (37.1). *)
Lemma transfer_indep X (rX := transversal_repr 1 X) :
is_transversal X HG G -> {in G, transfer =1 V rX}.