Section GringIrrMode.
Variable i : Iirr G.
Let n := irr_degree (socle_of_Iirr i).
Let mxZn_inj: injective (@scalar_mx algCfield n).

(* This is Isaacs, Theorem (3.8). *)
Theorem coprime_degree_support_cfcenter g :
coprime (truncC ('chi_i 1%g)) #|g ^: G| -> g \notin ('Z('chi_i))%CF ->
'chi_i g = 0.