End IntegralChar.
Section MoreIntegralChar.
Implicit Type gT : finGroupType.

(* This is Isaacs, Lemma (3.14). *)
(* Note that the assumption that G be cyclic is unnecessary, as S will be     *)
(* empty if this is not the case.                                             *)
Lemma sum_norm2_char_generators gT (G : {group gT}) (chi : 'CF(G)) :
let S := [pred s | generator G s] in
chi \is a character -> {in S, forall s, chi s != 0} ->
\sum_(s in S) `|chi s| ^+ 2 >= #|S|%:R.