Portal de Periódicos da CAPES

The Small Mathieu Groups

1999; Springer Nature; Linguagem: Inglês

10.1007/978-3-662-03891-8_17

2512-3254

Hans Cuypers, Leonard H. Soicher, Hans Sterk,

Advanced Topics in Algebra

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.