Characterization of classical groups by orbit sizes on the natural module

Liebeck, Martin

doi:10.1090/S0002-9939-96-03505-8

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

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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