Algebra and Logic

, Volume 35, Issue 6, pp 371–383 | Cite as

Minimal permutation representations of finite simple exceptional groups of typesG2 andF4

  • A. V. Vasilyev
Article

Abstract

A minimal permutation representation of a group is a faithful permutation representation of least degree. Well-studied to date are the minimal permutation representations of finite sporadic and classical groups for which degrees, point stabilizers, as well as ranks, subdegrees, and double stabilizers, have been found. Here we attempt to provide a similar account for finite simple ezceptional groups of types G2 and F4.

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References

  1. 1.
    V. D. Mazurov, “A minimal permutation representation of a simple Thompson group,”Algebra Logika,27, No. 5, 562–580 (1988).MATHMathSciNetGoogle Scholar
  2. 2.
    V. D. Mazurov, “Minimal permutation representations of finite simple classical groups. Special linear, symplectic, and unitary groups,”Algebra Logika,32, No. 3, 267–287 (1993).MATHMathSciNetGoogle Scholar
  3. 3.
    V. A. Vasilyev and V. D. Mazurov, “Minimal permutation representations of finite simple orthogonal groups,”Algebra Logika,33, No. 6, 603–627 (1994).Google Scholar
  4. 4.
    M. W. Liebeck and J. Saxl, “On the orders of maximal subgroups of the finite exceptional groups of Lie type,”Proc. London Math. Soc.,55, 299–300 (1987).MathSciNetGoogle Scholar
  5. 5.
    R. Steinberg,Lectures on Chevalley Groups, Yale University (1967).Google Scholar
  6. 6.
    R. W. Carter,Simple Groups of Lie Type, Wiley, New York (1972).Google Scholar
  7. 7.
    J. H. Conway, R. T. Curtis, S. P. Norton, et al.,Atlas of Finite Groups, Clarendon, Oxford (1985).Google Scholar

Copyright information

© Plenum Publihing Coporation 1996

Authors and Affiliations

  • A. V. Vasilyev

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