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.