Classes of Conjugate Involutions of Symplectic Groups over Fields of Even Order and Related Questions

We use an analogue of the Suzuki form in $PSL(n,q)$ in order to find representatives of conjugate involution classes of symplectic groups $Sp(2n,q)$ over fields of any even order. Let $\tau$ be an involution of a group $G$ and $ccw(G,\tau)$ denote the number of all conjugate and commutative involutions for $\tau$. We establish an uppen bound for this number in the case of $Sp(2n,q)$.