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arXiv · 1405.1258

Classification of subgroups of symplectic groups over finite fields containing a transvection

Sara Arias-de-Reyna·Luis Dieulefait·Gabor Wiese
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Abstract

In this note we give a self-contained proof of the following classification (up to conjugation) of subgroups of the general symplectic group of dimension n over a finite field of characteristic l, for l at least 5, which can be derived from work of Kantor: G is either reducible, symplectically imprimitive or it contains Sp(n, l). This result is for instance useful for proving "big image" results for symplectic Galois representations.

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Sara Arias-de-Reyna, Luis Dieulefait, Gabor Wiese. 2014-05-06. Classification of subgroups of symplectic groups over finite fields containing a transvection. https://arxiv.org/abs/1405.1258

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