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Finite simple groups and finite primitive permutation groups

Published online by Cambridge University Press:  17 April 2009

Cheryl E. Praeger
Cheryl E. Praeger
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, Western Australia 6009, Australia.
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Abstract

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The classification of the finite simple groups has had far-reaching consequences for many branches of algebra. This paper is a discussion of several problems about primitive permutation groups which have been solved using the simple group classification.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 355 - 365
Copyright
Copyright © Australian Mathematical Society 1983

References

[1]Aschbacher, M. and Scott, J.L., “Maximal subgroups of finite groups”, J. Algebra (to appear).Google Scholar
[2]Babai, L., “On the order of uniprimitive permutation groups”, Ann. of Math. (2) 113 (1981), 553–568.CrossRefGoogle Scholar
[3]Babai, L., “On the order of doubly transitive permutation groups”, Invent. Math. 65 (1982), 473–484.CrossRefGoogle Scholar
[4]Babai, L., Cameron, P.J. and Palfy, P.P., “On the orders of primitive groups with restricted nonabelian composition factors”, J. Algebra 79 (1982), 161–168.CrossRefGoogle Scholar
[5]Bochert, A., “Ueber die Zahl der verschiedenen Werthe, die eine Function gegebener Buchstaben durch Vertauschung derselben erlangen kann”, Math. Ann. 33 (1889), 584–590.CrossRefGoogle Scholar
[6]Cameron, P.J., “Finite permutation groups and finite simple groups”, Bull. London Math. Soc. 13 (1981), 1–22.CrossRefGoogle Scholar
[7]Cameron, P.J., Neumann, P.M. and Teague, D.N., “On the degrees of primitive permutation groups”, Math. Z. 180 (1982), 141–149.CrossRefGoogle Scholar
[8]Cameron, P.J., Praeger, C.E., Saxl, J. and Seitz, G.M., “On the Sims conjecture and distance transitive graphs”, Bull. London Math. Soc. 15 (1983), 499–506.CrossRefGoogle Scholar
[9]Carter, R.W., Simple groups of Lie type (John Wiley & Sons, London, New York, Sydney, 1972).Google Scholar
[10]Hurley, J.F. and Rudvalis, A., “Finite simple groups”, Amer. Math. Monthly 84 (1978), 693–714.CrossRefGoogle Scholar
[11]Jordan, C., “Sur la limite de transitivité des groupes non alternés”, Bull. Soc. Math. France 1 (1873), 40–71.Google Scholar
[12]Kovács, L.G., “Maximal subgroups in composite finite groups”, in preparation.Google Scholar
[13]Liebeck, M. and Saxl, J., “Primitive permutation groups containing an element of large prime order”, unpublished.Google Scholar
[14]Mathieu, E., “Mémoire sur l'étude des fonctions de plusieurs quantités, sur le manière de les former et sur les substitutions qui les laissent invariables”, J. Math. Pure Appl. (Liouville) (2) 6 (1861), 241–323.Google Scholar
[15]Miyamoto, I., “On primitive permutation groups of degree 2p = 4q + 2, p and q being prime numbers”, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 22 (1975), 17–23.Google Scholar
[16]Neumann, P.M. and Saxl, J., “The primitive permutation groups of some special degrees, II: small multiples of certain large primes”, Math. Z. 169 (1979), 205–222.CrossRefGoogle Scholar
[17]Praeger, C.E., “On elements of prime order in primitive permutation groups”, J. Algebra 60 (1979), 126–157.CrossRefGoogle Scholar
[18]Praeger, C.E. and Saxl, J., “On the orders of primitive permutation groups”, Bull. London Math. Soc. 12 (1980), 303–307.CrossRefGoogle Scholar
[19]Sims, C.C., “Computational methods in the study of permutation groups”, Computational problems in abstract algebra, 169–183 (Proc. Conf. Oxford, 1967. Pergamon, London, 1970).Google Scholar
[20]Thompson, J.G., “Bounds for orders of maximal subgroups”, J. Algebra 14 (1970), 135–138.CrossRefGoogle Scholar
[21]Wielandt, H., Finite permutation groups (Academic Press, New York, London, 1964).Google Scholar
[22]Wielandt, H., Permutation groups through invariant relations and invariant functions (Ohio State University Lecture Notes. Ohio State University, Columbus, Ohio, 1969).Google Scholar