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

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 impri...

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Bibliographic Details
Published in:arXiv.org 2014-05
Main Authors: Arias-de-Reyna, Sara, Dieulefait, Luis, Wiese, Gabor
Format: Article
Language:English
Subjects:
Classification
Conjugation
Fields (mathematics)
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422