Publications
151 results found
Liebeck MW, Shalev A, 2007, The sparsity of dimensions of irreducible representations of finite simple groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 39, Pages: 467-472, ISSN: 0024-6093
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- Citations: 1
Liebeck MW, O'Brien EA, 2007, Finding the characteristic of a group of lie type, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, Vol: 75, Pages: 741-754, ISSN: 0024-6107
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- Citations: 14
Liebeck MW, Seitz GM, 2005, Maximal subgroups of large rank in exceptional groups of Lie type, JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, Vol: 71, Pages: 345-361, ISSN: 0024-6107
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- Citations: 10
Liebeck MW, Shalev A, 2005, Fuchsian groups, finite simple groups and representation varieties, INVENTIONES MATHEMATICAE, Vol: 159, Pages: 317-367, ISSN: 0020-9910
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- Citations: 55
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
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
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
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.
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
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
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
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
Liebeck MW, Shalev A, 2003, Residual properties of free products of finite groups, JOURNAL OF ALGEBRA, Vol: 268, Pages: 286-289, ISSN: 0021-8693
Liebeck MW, Seitz GM, 2003, Variations on a theme of Steinberg, JOURNAL OF ALGEBRA, Vol: 260, Pages: 261-297, ISSN: 0021-8693
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- Citations: 14
Lawther R, Liebeck MW, Seitz GM, 2002, Fixed point spaces in actions of exceptional algebraic groups (vol 205, pg 339, 2002), PACIFIC JOURNAL OF MATHEMATICS, Vol: 207, Pages: 507-507, ISSN: 0030-8730
Lawther R, Liebeck MW, Seitz GM, 2002, Fixed point ratios in actions of finite exceptional groups of Lie type, PACIFIC JOURNAL OF MATHEMATICS, Vol: 205, Pages: 393-464, ISSN: 0030-8730
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- Citations: 51
Lawther R, Liebeck MW, Seitz GM, 2002, Fixed point spaces in actions of exceptional algebraic groups, PACIFIC JOURNAL OF MATHEMATICS, Vol: 205, Pages: 339-391, ISSN: 0030-8730
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- Citations: 21
Liebeck MW, Shalev A, 2002, Bases of primitive linear groups, JOURNAL OF ALGEBRA, Vol: 252, Pages: 95-113, ISSN: 0021-8693
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- Citations: 20
Liebeck MW, Praeger CE, Saxl J, 2002, Primitive permutation groups with a common suborbit, and edge-transitive graphs, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 84, Pages: 405-438, ISSN: 0024-6115
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- Citations: 5
Liebeck MW, Shalev A, 2002, Random (<i>r</i>, <i>s</i>)-generation of finite classical groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 34, Pages: 185-188, ISSN: 0024-6093
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- Citations: 16
Liebeck MW, Shalev A, 2001, Diameters of finite simple groups: sharp bounds and applications, ANNALS OF MATHEMATICS, Vol: 154, Pages: 383-406, ISSN: 0003-486X
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- Citations: 96
Liebeck MW, Pyber L, 2001, Finite linear groups and bounded generation, DUKE MATHEMATICAL JOURNAL, Vol: 107, Pages: 159-171, ISSN: 0012-7094
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- Citations: 23
Liebeck MW, Praeger CE, Saxl J, 2000, Transitive subgroups of primitive permutation groups, Journal of Algebra, Vol: 234, Pages: 291-361, ISSN: 0021-8693
Liebeck MW, Seitz GM, 1999, On finite subgroups of exceptional algebraic groups, JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, Vol: 515, Pages: 25-72, ISSN: 0075-4102
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- Citations: 49
Guralnick RM, Liebeck MW, Saxl J, et al., 1999, Random generation of finite simple groups, JOURNAL OF ALGEBRA, Vol: 219, Pages: 345-355, ISSN: 0021-8693
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- Citations: 10
Liebeck MW, Shalev A, 1999, Simple groups, permutation groups, and probability, Journal of the American Mathematical Society, Vol: 12, Pages: 497-520, ISSN: 0894-0347
Liebeck MW, 1998, The classification of finite linear spaces with flag-transitive automorphism groups of affine type, JOURNAL OF COMBINATORIAL THEORY SERIES A, Vol: 84, Pages: 196-235, ISSN: 0097-3165
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- Citations: 40
Liebeck MW, Seitz GM, 1998, On the subgroup structure of exceptional groups of Lie type, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 350, Pages: 3409-3482, ISSN: 0002-9947
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- Citations: 46
Lawther R, Liebeck MW, 1998, On the diameter of a Cayley graph of a simple group of Lie type based on a conjugacy class, JOURNAL OF COMBINATORIAL THEORY SERIES A, Vol: 83, Pages: 118-137, ISSN: 0097-3165
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- Citations: 25
Liebeck MW, Seitz GM, 1998, On the subgroup structure of classical groups, Inventiones Mathematicae, Vol: 134, Pages: 427-453, ISSN: 0020-9910
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