Symplectic Group

The symplectic group ${\it Sp}_n(q)$ for $n$ Even is the Group of elements of the General Linear Group ${\it GL}_n$ that preserve a given nonsingular Symplectic Form. Any such Matrix has Determinant 1.

See also General Linear Group, Lie-Type Group, Projective Symplectic Group, Symplectic Form

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it Sp}_n(q)$ and ${\it PSp}_n(q)={\it S}_n(q)$.'' §2.3 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, pp. x-xi, 1985.

Wilson, R. A. ``ATLAS of Finite Group Representation.'' http://for.mat.bham.ac.uk/atlas/html/contents.html#symp.