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Characterization of classical groups by orbit sizes on the natural module

Author(s): Martin W. Liebeck
Journal: Proc. Amer. Math. Soc. 124 (1996), 2961-2966.
MSC (1991): Primary 20G40
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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: 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
Copyright of article: Copyright 1996, American Mathematical Society

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