Steiner System - Mathieu Groups

Mathieu Groups

Several examples of Steiner systems are closely related to group theory. In particular, the finite simple groups called Mathieu groups arise as automorphism groups of Steiner systems:

  • The Mathieu group M11 is the automorphism group of a S(4,5,11) Steiner system
  • The Mathieu group M12 is the automorphism group of a S(5,6,12) Steiner system
  • The Mathieu group M22 is the unique index 2 subgroup of the automorphism group of a S(3,6,22) Steiner system
  • The Mathieu group M23 is the automorphism group of a S(4,7,23) Steiner system
  • The Mathieu group M24 is the automorphism group of a S(5,8,24) Steiner system.

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