Classification of Subgroups of Symplectic Groups Over Finite Fields Containing a Transvection

@article{AriasdeReyna2014ClassificationOS,
  title={Classification of Subgroups of Symplectic Groups Over Finite Fields Containing a Transvection},
  author={Sara Arias-de-Reyna and Luis V. Dieulefait and Gabor Wiese},
  journal={Demonstratio Mathematica},
  year={2014},
  volume={49},
  pages={129 - 148}
}
Abstract In this note, we give a self-contained proof of the following classification (up to conjugation) of finite subgroups of GSpn(F̅ℓ) containing a nontrivial transvection for ℓ ≥ 5, which can be derived from work of Kantor: G is either reducible, symplectically imprimitive or it contains Spn(F̅ℓ). This result is for instance useful for proving ‘big image’ results for symplectic Galois representations. 
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