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Published online by Cambridge University Press: 31 October 2024
We emphasize the unique position enjoyed by the Mathieu groups as the only quadruply or quintuply transitive permutation groups that exist, other than the alternating and symmetric groups. Their involvement in the largest Conway group ·O, the Monster group M and many other exceptional sporadic simple groups is mentioned. Brief descriptions of several of the most important constructions of the group M24 are given.
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