Symplectic group is perfect

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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 \ge 2 and k has at least three elements.

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

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