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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
DOI: https://doi.org/10.1090/S0002-9939-97-03801-X
MathSciNet review: 1376761
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Abstract | References | Similar Articles | Additional Information

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, Groupes et algèbres de Lie, Chapitres 3, §7, Exercises 5-8. MR 58:28083a
  • [F] W. Feit, Characters of finite groups, Benjamin, NY, Amsterdam (1967). MR 36:2715
  • [S] I. Schur, Collected Works, Springer-Verlag, Berlin, Heidelberg, N.Y. MR 57:2858a

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Additional Information

Walter Feit
Affiliation: Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
Email: feit@math.yale.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03801-X
Received by editor(s): November 1, 1995
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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