On subgroups of 𝑀₂₄. II. The maximal subgroups of 𝑀₂₄

Choi, Chang

doi:10.1090/S0002-9947-1972-0294473-2

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
DOI: https://doi.org/10.1090/S0002-9947-1972-0294473-2
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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