FINITE LINEAR-GROUPS AND THEOREMS OF MINKOWSKI AND SCHUR

Let G be a finite group with a faithful rational valued character of d egree n. A theorem of I. Schur gives a bound for the order of G in ter ms of n, generalizing an earlier result of H. Minkowski who showed tha t the same bound holds if G subset of or equal to GL(n, Q). This note contains strengthened versions of these results which in particular sh ow that a 2-subgroup of GL(n, Q) of maximum possible order contains a reflection.