Section Center.
Variable (gT : finGroupType) (G : {group gT}).
Implicit Types (phi chi : 'CF(G)) (H : {group gT}).
(* This is part of Isaacs (2.27)(b). *)
Fact cfcenter_group_set phi : group_set ('Z(phi))%CF.
Canonical cfcenter_group f := Group (cfcenter_group_set f).

(* This is Isaacs (2.30). *)
Lemma irr1_bound (i : Iirr G) :
('chi_i 1%g) ^+ 2 <= #|G : 'Z('chi_i)%CF|%:R
?= iff ('chi_i \in 'CF(G, 'Z('chi_i)%CF)).