End AbelianStructure.
Arguments abelian_type {gT} A%g.
Arguments homocyclic {gT} A%g.
Section IsogAbelian.
Variables aT rT : finGroupType.
Implicit Type (gT : finGroupType) (D G : {group aT}) (H : {group rT}).

(* Specifications: *)
Lemma isog_abelian_type G H : isog G H -> abelian_type G = abelian_type H.
Lemma eq_abelian_type_isog G H :
abelian G -> abelian H -> isog G H = (abelian_type G == abelian_type H).
Lemma isog_abelem_card p G H :
p.-abelem G -> isog G H = p.-abelem H && (#|H| == #|G|).