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On maximal subgroups of the Fischer group Fi22

Published online by Cambridge University Press:  24 October 2008

Robert A. Wilson
Robert A. Wilson
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, University of Cambridge
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Extract

In this paper we classify the maximal subgroups of the smallest Fischer group Fi22, which is a simple group of order 64561 751 654 400 = 217. 39. 52. 7. 11. 13. Although this is not a complete classification into conjugacy classes, it is for most practical purposes almost as good, since the exceptional cases are very small groups.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 197 - 222
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

REFERENCES

[1]Conway, J. H.. A construction for the smallest Fischer group. In Finite Groups '72 (Gagen, T., Hale, M. P. and Shult, E. E., Eds.). North-Holland, Amsterdam, 1972, 27–35.Google Scholar
[2]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A.. An atlas of finite groups. (In the Press.)Google Scholar
[3]Curtis, R. T.. A new combinatorial approach to M24. Math. Proc. Cambridge Philoa. Soc. 79 (1976), 25–42.CrossRefGoogle Scholar
[4]Enright, G. M.. The structure and subgroups of the Fischer groups F22 and F23. Ph.D. thesis, Cambridge, 1976.Google Scholar
[5]Enright, G. M.. A description of the Fischer group F22. J. Algebra 46 (1977), 334–343.CrossRefGoogle Scholar
[6]Enright, G. M.. Subgroups generated by transpositions in F22 and F 23. Comm. Algebra 6 (1978), 823–837.CrossRefGoogle Scholar
[7]Fischer, B.. Finite groups generated by 3-transpositions. (Preprint.)Google Scholar
[8]Flaass, D.. 2-local subgroups of Fischer's groups. Mat. Zametki 35 (1984), 333–342.Google Scholar
[9]Hunt, D. C.. Character tables of certain finite simple groups. Bull. Austral. Math. Soc. 5 (1971), 1–42.CrossRefGoogle Scholar
[10]List, R.. Maximal subgroups of U6 (2). (Unpublished.)Google Scholar
[11]Norton, S. P. and Wilson, R. A.. Maximal subgroups of 08+(2). (Unpublished.)Google Scholar
[12]Tchakerian, K. B.. Maximal subgroups of the Tits simple group. (Preprint.)Google Scholar
[13]Wilson, R. A.. Maximal subgroups of some sporadic simple groups. Ph.D. thesis, Cambridge, 1982.Google Scholar
[14]Wilson, R. A.. The geometry and maximal subgroups of the simple groups of Tits and Rudvalis. Proc. London Math. Soc. (1984)CrossRefGoogle Scholar
[15]Wilson, R. A.. On maximal subgroups of automorphism groups of simple groups. (Preprint.)Google Scholar
[16]Wilson, R. A.. Maximal subgroups of Conway's group Co., J. Algebra 85 (1984), 144–165.CrossRefGoogle Scholar