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Mathieu group
In mathematics, the Mathieu groups were the first known sporadic groups. The largest of them, M24, is the automorphism group of the binary Golay code, i.e., the group of permutations of coordinates mapping W to itself. We can also regard it as the intersection of S24 and Stab(W) in Aut(V). This is a finite simple group. The simple subgroups M23, M22, M12, and M11 can be defined as the stabilizers in M24 of a single coordinate, an ordered pair of coordinates, a 12-element subset of the coordinates corresponding to a code word, and a 12-element code word together with a single coordinate, respectively.
References
- Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; Wilson, R. A. (1985). Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups. With computational assistance from J. G. Thackray. Eynsham: Oxford University Press. ISBN 0-19-853199-0
Referenced By
Binary Golay code | Classification of finite simple groups | Fischer group | List of group theory topics | List of mathematical topics (M-O) | Sporadic group
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