Classification of finite N-groups

From Groupprops
Jump to: navigation, search

Statement

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).

Related facts

References

Journal references