# Projective symplectic group is simple

From Groupprops

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

## Statement

Suppose is a positive integer and is a field. Then, the projective symplectic group is a simple group except in the following three cases: and has two elements, and has three elements, and has two elements. In other words, the three exceptions are .