Classification of finite N-groups

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Any finite N-group that is not solvable is an almost simple group. In particular, it contains a simple normal centralizer-free subgroup isomorphic to one of the following:

  1. The projective special linear group PSL(2,q) for some prime power q > 3.
  2. The Suzuki group Sz(2^{2n + 1}), n \ge 1.
  3. The projective special linear group PSL(3,3).
  4. The Mathieu group M_{11}.
  5. The alternating group of degree seven A_7.
  6. The projective special unitary group PSU(3,3).

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