Isomorphism between symplectic and projective symplectic group in characteristic two
Suppose is a field and is a positive integer. The following are equivalent:
- has characteristic two.
- The symplectic group is a centerless group.
- The natural quotient map from the symplectic group to the projective symplectic group is an isomorphism of groups.
- The symplectic group and projective symplectic group are isomorphic groups.
In any other characteristic, the center of is cyclic of order two.