Classification of subgroups of symplectic groups over finite fields containing a transvection
Number Theory
2014-05-07 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.1405.1258,
title = {Classification of subgroups of symplectic groups over finite fields containing a transvection},
author = {Sara Arias-de-Reyna and Luis Dieulefait and Gabor Wiese},
journal= {arXiv preprint arXiv:1405.1258},
year = {2014}
}
Comments
17 pages. This manuscript is extracted from an old version of our paper arXiv:1203.6552