Finite linear groups and theorems of Minkowski and Schur

Walter Feit

Proc. Amer. Math. Soc. 125 (1997), pp. 1259-1262 

Abstract. Let G be a finite group with a faithful rational valued character of 
degree n. A theorem of I. Schur gives a bound for the order of G in terms of n,
generalizing an earlier result of H. Minkowski who showed that the same bound 
holds if G \subseteq GL(n,Q). This note contains strengthened versions of these
results which in particular show that a 2-subgroup of GL(n,Q) of maximum 
possible order contains a reflection.