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Characterization of classical groups by orbit sizes on the natural module
Authors:Martin W. Liebeck
Affiliation:Department of Mathematics, Imperial College, London SW7 2BZ, United Kingdom
Abstract:We show that if $V$ is a finite vector space, and $G$ is a subgroup of $PGamma L(V)$ 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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