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Transactions of the American Mathematical Society

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On subgroups of $ M\sb{24}$. II. The maximal subgroups of $ M\sb{24}$

Author: Chang Choi
Journal: Trans. Amer. Math. Soc. 167 (1972), 29-47
MSC: Primary 20B20
MathSciNet review: 0294473
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Abstract: In this paper we effect a systematic study of transitive subgroups of $ {M_{24}}$, obtaining 5 transitive maximal subgroups of $ {M_{24}}$ of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of $ {M_{24}}$. I, enable us to enumerate all the maximal subgroups of $ {M_{24}}$. There are, up to conjugacy, nine of them. The complete list includes one more in addition to those listed by J. A. Todd in his recent work on $ {M_{24}}$. The two works were done independently employing completely different methods.

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Keywords: Mathieu groups, 5-fold transitive permutation groups, maximal subgroups, primitive representations
Article copyright: © Copyright 1972 American Mathematical Society

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