Projective symplectic group is simple

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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 m is a positive integer and k is a field. Then, the projective symplectic group PSp(2m,k) is a simple group except in the following three cases: m = 1 and k has two elements, m = 1 and k has three elements, m = 2 and k has two elements. In other words, the three exceptions are PSp(2,2),PSp(2,3),PSp(4,2).

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