Classification Of Subgroups Of Symplectic Groups Over Finite Fields Containing A Transvection

DEMONSTRATIO MATHEMATICA(2016)

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Abstract
In this note, we give a self-contained proof of the following classification (up to conjugation) of finite subgroups of GSp(n)((F) over bar (l)) containing a nontrivial transvection for l >= 5, which can be derived from work of Kantor: G is either reducible, symplectically imprimitive or it contains Sp(n)(F-l). This result is for instance useful for proving 'big image' results for symplectic Galois representations.
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Key words
sympletic group over a finite field, transvection, classification of subgroups of linear groups
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