Products of involutions in symplectic groups I: bireflections

Abstract

We classify bireflectional elements (products of 2 involutions) in symplectic groups Sp$(2n,K)$ over a field $K$. We also classify rev ersible elements (elements conjugate to their inverses) and bireflectional elements in finite projective symplectic groups PSp$(2n,q)$.

10 pages