End MorphPcore.
Section EqPcore.
Variables gT : finGroupType.
Implicit Types (pi rho : nat_pred) (G H : {group gT}).

Lemma bigcap_p'core pi G :
G :&: \bigcap_(p < #|G|.+1 | (p : nat) \in pi) 'O_p^'(G) = 'O_pi^'(G).