Section MorphPcore.
Implicit Types (pi : nat_pred) (gT rT : finGroupType).
Canonical pcore_igFun pi := [igFun by pcore_sub pi & morphim_pcore pi].
Canonical pcore_gFun pi := [gFun by morphim_pcore pi].
Canonical pcore_pgFun pi := [pgFun by morphim_pcore pi].
End PcoreMod.

Lemma pseries_pop2 pi1 pi2 gT (G : {group gT}) :
'O_pi1(G) = 1 -> 'O_{pi1, pi2}(G) = 'O_pi2(G).