Mathieu Group

Mathieu Group

In mathematics, the Mathieu groups M₁₁, M₁₂, M₂₂, M₂₃, M₂₄, introduced by Mathieu (1861, 1873), are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They were the first sporadic simple groups discovered.

Sometimes the notation M₁₀, M₂₀ and M₂₁ is used for related groups (which act on sets of 10, 20, and 21 points, respectively), namely the stabilizers of points in the larger groups. While these are not sporadic simple groups, they are subgroups of the larger groups and can be used to construct the larger ones. John Conway has shown that one can also extend this sequence up, obtaining the Mathieu groupoid M₁₃ acting on 13 points.