Mathieu groups | Wikipedia audio article

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00:00:35 1 History
00:01:11 2 Multiply transitive groups
00:01:46 2.1 Order and transitivity table
00:02:04 3 Constructions of the Mathieu groups
00:02:40 3.1 Permutation groups
00:03:16 3.2 Automorphism groups of Steiner systems
00:03:51 3.3 Automorphism groups on the Golay code
00:04:27 3.4 Dessins d'enfants



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SUMMARY
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In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu (1861, 1873). They are multiply transitive permutation groups on 11, 12, 22, 23 or 24 objects. They were the first sporadic groups to be discovered.
Sometimes the notation M9, M10, M20 and M21 is used for related groups (which act on sets of 9, 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. M21 is simple, but is not a sporadic group, being isomorphic to PSL(3,4).