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Finite and Locally Finite Groups pp 97–110Cite as

Finite Simple Groups and Permutation Groups

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Part of the book series: NATO ASI Series ((ASIC,volume 471))

Abstract

This paper surveys some results in the area of maximal subgroups of the finite simple groups and their automorphism groups. The first two sections are concerned with maximal subgroups of the alternating and symmetric groups. We outline the Reduction Theorem and discuss the maximality of primitive groups in the corresponding symmetric groups. In the third section we consider the corresponding questions for the classical groups. The next section contains a brief survey of knowledge of the maximal subgroups of the other almost simple groups. Finally, the last section outlines some recent work on primitive permutation groups of special degrees.

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Author information

Authors and Affiliations

  1. DPMMS, Cambridge University, 16 Mill Lane, Cambridge, CB2 1SB, England

    J. Saxl

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  1. J. Saxl
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Manchester, Manchester, UK

    B. Hartley

  2. Department of Mathematics, University of Oregon, Eugene, Oregon, USA

    G. M. Seitz

  3. UMIST, Manchester, UK

    A. V. Borovik  & R. M. Bryant  & 

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Saxl, J. (1995). Finite Simple Groups and Permutation Groups. In: Hartley, B., Seitz, G.M., Borovik, A.V., Bryant, R.M. (eds) Finite and Locally Finite Groups. NATO ASI Series, vol 471. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0329-9_4

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  • DOI: https://doi.org/10.1007/978-94-011-0329-9_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4145-4

  • Online ISBN: 978-94-011-0329-9

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