Canonical Fitting_igFun := [igFun by Fitting_sub & morphim_Fitting].
Canonical Fitting_gFun := [gFun by morphim_Fitting].
Canonical Fitting_pgFun := [pgFun by morphim_Fitting].
Section IsoFitting.
Variables (gT rT : finGroupType) (G D : {group gT}) (f : {morphism D >-> rT}).

Lemma abelem_split_dprod rT p (A B : {group rT}) :
p.-abelem A -> B \subset A -> exists C : {group rT}, B \x C = A.