(* There are no general morphism relations for the p-rank. We later prove     *)
(* some relations for the p-rank of a quotient in the QuotientAbelem section. *)
Section InjmAbelem.
Variables (aT rT : finGroupType) (D G : {group aT}) (f : {morphism D >-> rT}).
Hypotheses (injf : 'injm f) (sGD : G \subset D).
Let defG : invm injf @* (f @* G) = G := morphim_invm injf sGD.

(* Specifications: *)
Lemma exponent_injm : exponent (f @* G) = exponent G.
Lemma injm_abelem p : p.-abelem (f @* G) = p.-abelem G.
Lemma injm_pnElem p n (E : {group aT}) :
E \subset D -> ((f @* E)%G \in 'E_p^n(f @* G)) = (E \in 'E_p^n(G)).
Lemma injm_pmaxElem p (E : {group aT}) :
E \subset D -> ((f @* E)%G \in 'E*_p(f @* G)) = (E \in 'E*_p(G)).
Lemma injm_grank : 'm(f @* G) = 'm(G).
Lemma injm_rank : 'r(f @* G) = 'r(G).
End InjmAbelem.