Symplectic group is perfect

This article gives the statement, and possibly proof, of a particular group or type of group (namely, Symplectic group (?)) satisfying a particular group property (namely, Perfect group (?)).

Statement

The symplectic group $Sp(2m,k)$ is a perfect group if either of these conditions hold:

• $k$ has at least four elements.
• $m\geq 2$ and $k$ has at least three elements.

In other words, the only exceptions are $Sp(2,2),Sp(2,3),Sp(4,2)$.

Related facts

• Special linear group is perfect
• Commutator subgroup of general linear group is special linear group
• Commutator subgroup of orthogonal group is special orthogonal group