Abstract
Let b be a nondegenerate symplectic form on a vector space V over a finite field. It is well-known that every intermediate group between Sp(V,b) and ΓSp(V,b) (i.e. the isometry and the semisimilarity groups of b, respectively) is Rank 3 in its action on the projective space P(V). We prove that this property characterizes such subgroups of ΓSp(V,b) when the dimension of V is greater than 2.
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Abhyankar, S.S., Inglis, N.F.J., Yalcin, U.D. (2005). Supplementary Thoughts on Symplectic Groups. In: Voelklein, H., Shaska, T. (eds) Progress in Galois Theory. Developments in Mathematics, vol 12. Springer, Boston, MA. https://doi.org/10.1007/0-387-23534-5_1
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DOI: https://doi.org/10.1007/0-387-23534-5_1
Publisher Name: Springer, Boston, MA
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