Rational projective representations of finite groups

Abstract

Let G bea finite group, let C1, …, Cn be the cyclic subgroups of G and let 1i be the identity linear character of Ci (1 ≤ i ≤ n). It is a well-known result of Artin ((l), 39·1) that a character x of a linear representation of G over the rational numbers may be writtenwhere a1, …, an are integers. In this note, we establish an analogue of this result for characters of projective representations over the rational numbers.