Abstract
In this project we use the tools and techniques from Chapter 8 to construct the small Mathieu groups M 10, M 11 and M 12. These groups were discovered by the French mathematician Emile Mathieu (1835–1890), who also discovered the large Mathieu groups M 22, M 23 and M 24. See [9, 10, 11]. They are remarkable groups: for example, apart from the symmetric and alternating groups, M 12 and M 24 are the only 5-transitive permutation groups. The group Mio has a normal subgroup of index 2 isomorphic to A6. The other five groups are among the 26 sporadic simple groups, occurring in the classification of finite simple groups. After Mathieu’s discovery of these five sporadic simple groups it took almost a century before the sixth sporadic simple group was found.
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Cuypers, H., Soicher, L.H., Sterk, H. (1999). The Small Mathieu Groups. In: Cohen, A.M., Cuypers, H., Sterk, H. (eds) Some Tapas of Computer Algebra. Algorithms and Computation in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03891-8_17
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DOI: https://doi.org/10.1007/978-3-662-03891-8_17
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