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Overgroups of Special Elements in Simple Algebraic Groups and Finite Groups of Lie Type

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Algebraic Groups and their Representations

Part of the book series: NATO ASI Series ((ASIC,volume 517))

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Abstract

In the last twenty years there has been a tremendous amount of progress in our understanding of subgroup structure of simple groups G, both algebraic over an algebraically closed field and finite. If G is of exceptional type, the progress has been particularly impressive, largely due to the work of Liebeck and Seitz; an excellent survey is the article [25] of Liebeck in this volume. If G is a finite classical simple group, the reduction theorem of Aschbacher [1] enables us to concentrate on the case where the subgroup H is almost simple modulo the subgroup Z of scalars and the (projective) representation of the simple group F* (H/Z) on the natural module V for G is absolutely irreducible. There is a similar reduction theorem for G a classical algebraic group over an algebraically closed field [28]. There are a number of survey articles where the situation is discussed — see, e.g., [21], [24], [35], and [39].

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Authors and Affiliations

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

    J. Saxl

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  1. Mathematics Institute, University of Warwick, Coventry, UK

    R. W. Carter

  2. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, UK

    J. Saxl

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Saxl, J. (1998). Overgroups of Special Elements in Simple Algebraic Groups and Finite Groups of Lie Type. In: Carter, R.W., Saxl, J. (eds) Algebraic Groups and their Representations. NATO ASI Series, vol 517. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5308-9_16

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  • DOI: https://doi.org/10.1007/978-94-011-5308-9_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-5292-1

  • Online ISBN: 978-94-011-5308-9

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