Rank three symplectic groups

Umud Devrim Yalcin, Purdue University

Abstract

Let b be a nondegenerate symplectic form on a vector space V over a finite field. Every intermediate group between the isometry and the semisimilarity groups of b (i.e. every symplectic group containing Sp(V,b)) is Rank 3 in its action on the projective space [special characters omitted](V). Here, it is proven that this property characterizes such symplectic groups when the dimension of V is greater than 2. There is only one exception to this theorem, and that occurs when the dimension is 4 and the order of the field is 2.

Degree

Ph.D.

Advisors

Abhyankar, Purdue University.

Subject Area

Mathematics

COinS