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

(* Specifications: *)
Lemma cfInd_char chi : chi \is a character -> 'Ind[G] chi \is a character.
Lemma cfInd_eq0 chi :
H \subset G -> chi \is a character -> ('Ind[G] chi == 0) = (chi == 0).
Lemma Ind_irr_neq0 i : H \subset G -> 'Ind[G, H] 'chi_i != 0.
(* 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.
Lemma cfker_Ind_irr i :
H \subset G -> cfker ('Ind[G, H] 'chi_i) = gcore (cfker 'chi_i) G.