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• Journal article
  Liebeck MW, Shalev A, 2005,

  Character degrees and random walks in finite groups of lie type

  , PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 90, Pages: 61-86, ISSN: 0024-6115
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  • Citations: 67
• Journal article
  Liebeck MW, Martin BM, Shalev A, 2005,

  On conjugacy classes of maximal subgroups of finite simple groups, and a related zeta function

  , Duke Mathematical Journal, Vol: 128, Pages: 541-557, ISSN: 0012-7094
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• Journal article
  Evans DM, 2004,

  Block transitive Steiner systems with more than one point orbit

  , Journal of Combinatorial Designs, Vol: 12, Pages: 459-465, ISSN: 1063-8539

  For all 'reasonable' finite t; k, and s, we construct a t-(א0,k, 1) design and a group of automorphisms which is transitive on blocks and has s orbits on points. In particular, there is a 2-(א0, 4, 1) design with a block-transitive group of automorphisms having two point orbits. This answers a question of P. J. Cameron and C. E. Praeger. The construction is presented in a purely combinatorial way, but is a by-product of a new way of looking at a model-theoretic construction of E. Hrushovski. © 2004 Wiley Periodicals, Inc.

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  • Citations: 7
• Journal article
  Liebeck MW, Shalev A, 2004,

  Fuchsian groups, coverings of Riemann surfaces, subgroup growth, random quotients and random walks

  , JOURNAL OF ALGEBRA, Vol: 276, Pages: 552-601, ISSN: 0021-8693
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  • Citations: 64
• Journal article
  Liebeck MW, Seitz GM, 2004,

  The maximal subgroups of positive dimension in exceptional algebraic groups

  , MEM AM MATH SOC, Vol: 169, Pages: 1-227, ISSN: 0065-9266

  In this paper we complete the determination of the maximal subgroups of positive dimension in simple algebraic groups of exceptional type over algebraically closed fields. This follows work of Dynkin, who solved the problem in characteristic zero, and Seitz who did likewise over fields whose characteristic is not too small.A number of consequences are obtained. It follows from the main theorem that a simple algebraic group over an algebraically closed field has only finitely many conjugacy classes of maximal subgroups of positive dimension. It also follows that the maximal subgroups of sufficiently large order in finite exceptional groups of Lie type are known.

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• Journal article
  Liebeck MW, Testerman DM, 2004,

  Irreducible subgroups of algebraic groups

  , QUARTERLY JOURNAL OF MATHEMATICS, Vol: 55, Pages: 47-55, ISSN: 0033-5606
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  • Citations: 20
• Journal article
  Liebeck MW, Shalev A, 2004,

  The number of homomorphisms from a finite group to a general linear group

  , COMMUNICATIONS IN ALGEBRA, Vol: 32, Pages: 657-661, ISSN: 0092-7872
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  • Citations: 2
• Journal article
  Liebeck MW, Seitz GM, 2004,

  Subgroups of exceptional algebraic groups which are irreducible on an adjoint or minimal module

  , JOURNAL OF GROUP THEORY, Vol: 7, Pages: 347-372, ISSN: 1433-5883
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  • Citations: 13
• Journal article
  Liebeck MW, Shalev A, 2003,

  Residual properties of free products of finite groups

  , JOURNAL OF ALGEBRA, Vol: 268, Pages: 286-289, ISSN: 0021-8693
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• Journal article
  Liebeck MW, Shalev A, 2003,

  Residual properties of the modular group and other free products

  , JOURNAL OF ALGEBRA, Vol: 268, Pages: 264-285, ISSN: 0021-8693
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  • Citations: 5

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