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Proceedings of the American Mathematical Society

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

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Characterization of classical groups by orbit sizes on the natural module
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by Martin W. Liebeck PDF
Proc. Amer. Math. Soc. 124 (1996), 2961-2966 Request permission


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
  • MR Author ID: 113845
  • ORCID: 0000-0002-3284-9899
  • Email:
  • Received by editor(s): March 20, 1995
  • Communicated by: Ronald M. Solomon
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 2961-2966
  • MSC (1991): Primary 20G40
  • DOI:
  • MathSciNet review: 1343709