Classification of Subgroups of Symplectic Groups Over Finite Fields Containing a Transvection
Classification of Subgroups of Symplectic Groups Over Finite Fields Containing a Transvection
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包含平移的有限域上辛群子群的分类
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
G. Wiese
中科院分区：
文献类型：
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作者：
S. Arias;L. Dieulefait;G. Wiese
摘要本文给出了一类有限子群GSpn（F′ll）的自包含分类（直到共轭），该分类可由Kantor的工作导出：G或可约，或辛非原，或包含Spn（F′ll l）。例如，这个结果对于证明辛伽罗瓦表示的“大图像”结果很有用。
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.