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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

[1] W. Burnside, Theory of groups of finite order, Dover Publications, Inc., New York, 1955. 2d ed. MR 0069818
[2] R. D. Carmichael, Introduction to the theory of groups of finite order, Ginn, Boston, Mass., 1937.
[3] Chang Choi, On subgroups of 𝑀₂₄. I. Stabilizers of subsets, Trans. Amer. Math. Soc. 167 (1972), 1–27. MR 0294472, https://doi.org/10.1090/S0002-9947-1972-0294472-0
[4] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR 0224703
[5] C. Jordan, Traité des substitutions et des équations algébriques, Gauthier-Villars, Paris, 1870.
[6] Dudley E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, Oxford University Press, New York, 1940. MR 0002127
[7] G. A. Miller, Collected works. Vol . I, Univ. of Illinois Press, Urbana, Ill., 1935.
[8] Helmut Wielandt, Finite permutation groups, Translated from the German by R. Bercov, Academic Press, New York-London, 1964. MR 0183775
[9] E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1937), 256-264.