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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Characterization of classical groups
by orbit sizes on the natural module


Author: Martin W. Liebeck
Journal: Proc. Amer. Math. Soc. 124 (1996), 2961-2966
MSC (1991): Primary 20G40
MathSciNet review: 1343709
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Abstract: We show that if $V$ is a finite vector space, and $G$ is a subgroup of $P\Gamma L(V)$ having the same orbit sizes on 1-spaces as an orthogonal or unitary group on $V$, then, with a few exceptions, $G$ is itself an orthogonal or unitary group on $V$.


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Additional Information

Martin W. Liebeck
Affiliation: Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom
Email: m.liebeck@ic.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03505-8
PII: S 0002-9939(96)03505-8
Received by editor(s): March 20, 1995
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1996 American Mathematical Society