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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Finite linear groups and theorems
of Minkowski and Schur

Author: Walter Feit
Journal: Proc. Amer. Math. Soc. 125 (1997), 1259-1262
MSC (1991): Primary 20C15; Secondary 20H20
MathSciNet review: 1376761
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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 $G\subseteq GL(n,\mathbf {Q})$. This note contains strengthened versions of these results which in particular show that a $2$-subgroup of $GL(n,\mathbf {Q})$ of maximum possible order contains a reflection.

References [Enhancements On Off] (What's this?)

  • [B] N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Hermann, Paris, 1972. Actualités Scientifiques et Industrielles, No. 1349. MR 0573068
  • [F] Walter Feit, Characters of finite groups, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR 0219636
  • [S] Issai Schur, Gesammelte Abhandlungen. Band I, Springer-Verlag, Berlin-New York, 1973 (German). Herausgegeben von Alfred Brauer und Hans Rohrbach. MR 0462891

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Additional Information

Walter Feit
Affiliation: Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283

Received by editor(s): November 1, 1995
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society