End Center.
Section Induced.
Variables (gT : finGroupType) (G H : {group gT}).
Implicit Types (phi : 'CF(G)) (chi : 'CF(H)).

(* This is Isaacs Lemma (5.11). *)
Lemma cfker_Ind chi :
H \subset G -> chi \is a character -> chi != 0 ->
cfker ('Ind[G, H] chi) = gcore (cfker chi) G.