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

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.

17 pages. This manuscript is extracted from an old version of our paper arXiv:1203.6552

References in corpus (1)

• Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations