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.
Read more about this topic: Steiner System
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