About a question concerning Q-groups Original Research Article

A Q-group is a finite group all of whose ordinary complex representations have rationally valued characters. Let G be a solvable Q-group so that the Schur index mR(χ) = 1 for all χ set membership, variant Irr(G). In [3, Note 1, p. 285] Gow asks if not, under these conditions, already mQ(χ) = 1 for all χ set membership, variant Irr(G). In this paper we shall prove that the answer of this question is positive. The notations and definitions will be those of [6].