On subgroups of . II. The maximal subgroups of
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 | References | Similar Articles | Additional Information
Abstract: In this paper we effect a systematic study of transitive subgroups of , obtaining 5 transitive maximal subgroups of
of which one is primitive and four imprimitive. These results, along with the results of the paper, On subgroups of
. I, enable us to enumerate all the maximal subgroups of
. 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
. The two works were done independently employing completely different methods.
- [1] W. S. Burnside, Theory of groups of finite order, 2nd ed., 1911; reprint, Dover, New York, 1955. MR 16, 1086. MR 0069818 (16:1086c)
- [2] R. D. Carmichael, Introduction to the theory of groups of finite order, Ginn, Boston, Mass., 1937.
- [3]
Chang Choi, On subgroups of
. I: Stabilizers of subsets, Trans. Amer. Math. Soc. 167 (1972), 1-27. MR 0294472 (45:3542)
- [4] B. Huppert, Endliche Gruppen. I, Die Grundlehren der math. Wissenschaften, Band 134, Springer-Verlag, Berlin and New York, 1967. MR 37 #302. MR 0224703 (37:302)
- [5] C. Jordan, Traité des substitutions et des équations algébriques, Gauthier-Villars, Paris, 1870.
- [6] D. E. Littlewood, The theory of group characters and matrix representations of groups, Oxford Univ. Press, New York, 1940. MR 2, 3. MR 0002127 (2:3a)
- [7] G. A. Miller, Collected works. Vol . I, Univ. of Illinois Press, Urbana, Ill., 1935.
- [8] H. Wielandt, Finite permutation groups, Lectures, University of Tübingen, 1954/55; English transl., Academic Press, New York, 1964. MR 32 #1252. MR 0183775 (32:1252)
- [9] E. Witt, Die 5-fach transitiven Gruppen von Mathieu, Abh. Math. Sem. Univ. Hamburg 12 (1937), 256-264.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1972-0294473-2
Keywords:
Mathieu groups,
5-fold transitive permutation groups,
maximal subgroups,
primitive representations
Article copyright:
© Copyright 1972
American Mathematical Society