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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

The maximal orders of finite subgroups in $GL_{n}(\mathbf{Q})$

Author(s): Shmuel Friedland
Journal: Proc. Amer. Math. Soc. 125 (1997), 3519-3526.
MSC (1991): Primary 20C10, 20G30
MathSciNet review: 1443385
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Abstract | References | Similar articles | Additional information

Abstract: We give a relatively simple proof that the orthogonal group over the integers is the unique finite subgroup (up to a conjugation) in $GL_{n}(\mathbf{Z})$ of the maximal order for $n>>1$.


References:

[C-R]
C.W. Curtis and I. Reiner, Methods of representation theory I, J. Wiley, 1981. MR 82i:20001
[Fei]
W. Feit, The orders of finite linear groups, preprint 1995.
[Fri]
S. Friedland, Discrete groups of unitary isometries and balls in hyperbolic manifolds, Linear Algebra Appl., 241-243 (1996), 305-341. CMP 96:15
[Kat]
Y. Katznelson, On the orders of finite subgroups of $GL(n,{\mathbf{Z}})$, preprint, 1994.
[Min]
H. Minkowski, Collected Works I, 212-218.
[R-T]
D.N. Rockmore and K.S. Tan, A note on the order of finite subgroups of $GL(n,{\mathbf{Z}})$, Arch. Math. 64 (1995), 283-288. MR 95k:20075
[Ser]
J.P. Serre, Lie algebras and Lie groups, 2nd ed., Springer-Verlag, Berlin, 1992. MR 93h:17001
[Wei1]
B. Weisfeiler, Post-classification of Jordan's theorem on finite linear groups, Proc. Natl. Acad. Sci. USA, 81 (1984), 5278- 5279. MR 85j:20041
[Wei2]
B. Weisfeiler, On the size and structure of finite linear groups, preprint.


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Additional Information:

Shmuel Friedland
Affiliation: Department of Mathematics, University of Illinois at Chicago, Chicago, Illinois 60607-7045
Email: friedlan@uic.edu

DOI: 10.1090/S0002-9939-97-04283-4
PII: S 0002-9939(97)04283-4
Received by editor(s): August 5, 1996
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1997, American Mathematical Society




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