Imperial College London
Professor Martin Liebeck

ProfessorMartinLiebeck

Faculty of Natural Sciences, Department of Mathematics

Head of Pure Mathematics Section/Prof of Pure Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 8490m.liebeck Website

 
 
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Location

 

665Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
to

151 results found

Liebeck MW, 2016, Character ratios for finite groups of Lie type, and applications, Contemporary Mathematics, Vol: 694, ISSN: 0271-4132

For a nite groupG, acharacter ratiois a complex number of the form (x) (1),wherex2Gand is an irreducible character ofG. Upper bounds for absolutevalues of character ratios, particularly for simple groups, have long been of interest,for various reasons; these include applications to covering numbers, mixing timesof random walks, and the study of word maps. In this article we shall survey someresults on character ratios for nite groups of Lie type, and their applications.Character ratios for alternating and symmetric groups have been studied in greatdepth also { see for example [32, 33] { culminating in the de nitive results andapplications to be found in [20]; but we shall not discuss these here.It is not hard to see the connections between character ratios and group struc-ture. Here are three well known, elementary results illustrating these connections.The rst two go back to Frobenius. Denote by Irr(G) the set of irreducible charac-ters ofG.

Journal article

Gonshaw S, Liebeck MW, O'Brien E, 2016, Unipotent class representatives for finite classical groups, Journal of Group Theory, Vol: 20, Pages: 505-525, ISSN: 1435-4446

We describe explicitly representatives of the conjugacy classes ofunipotent elements of the finite classical groups.

Journal article

Liebeck MW, Seitz GM, Testerman DM, 2015, Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups, Pacific Journal of Mathematics, Vol: 279, Pages: 357-382, ISSN: 0030-8730

For G a simple algebraic group over an algebraically closed field of characteristic 0, we determine the irreducible representations ρ:G→I(V), where I(V) denotes one of the classical groups SL(V), Sp(V), SO(V), such that ρ sends some distinguished unipotent element of G to a distinguished element of I(V). We also settle a base case of the general problem of determining when the restriction of ρ to a simple subgroup of G is multiplicity-free.

Journal article

Liebeck MW, O'Brien EA, 2015, Recognition of finite exceptional groups of Lie type, Transactions of the American Mathematical Society, Vol: 368, Pages: 6189-6226, ISSN: 1088-6850

Let q be a prime power and let G be an absolutely irreducible subgroup ofGLd(F), where F is a finite field of the same characteristic as Fq, the field of q elements. Assume that G ∼= G(q), a quasisimple group of exceptional Lie type over Fq which is neither a Suzuki nor a Ree group. We present a Las Vegas algorithm that constructs an isomorphism from G to the standard copy of G(q). If G 6∼=3D4(q) with q even, then the algorithm runs in polynomial time, subject to the existence of a discrete log oracle.

Journal article

Giudici M, Liebeck MW, Praeger CE, Saxl J, Pham HTet al., 2015, Arithmetic results on orbits of linear groups, Transactions of the American Mathematical Society, Vol: 368, Pages: 2415-2467, ISSN: 1088-6850

Journal article

Liebeck MW, 2015, On products of involutions in finite groups of Lie type in even characteristic, JOURNAL OF ALGEBRA, Vol: 421, Pages: 431-437, ISSN: 0021-8693

Journal article

Liebeck MW, Shalev A, 2015, On fixed points of elements in primitive permutation groups, JOURNAL OF ALGEBRA, Vol: 421, Pages: 438-459, ISSN: 0021-8693

Journal article

Liebeck MW, Shalev A, 2014, POWER SETS AND SOLUBLE SUBGROUPS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 142, Pages: 3757-3760, ISSN: 0002-9939

Journal article

Lawther R, Liebeck MW, Seitz GM, 2014, Outer unipotent classes in automorphism groups of simple algebraic groups, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 109, Pages: 553-595, ISSN: 0024-6115

Journal article

Liebeck MW, Shalev A, 2014, Bases of primitive linear groups II, JOURNAL OF ALGEBRA, Vol: 403, Pages: 223-228, ISSN: 0021-8693

Journal article

Liebeck MW, Shalev A, 2013, POWERS IN FINITE GROUPS AND A CRITERION FOR SOLUBILITY, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 141, Pages: 4179-4189, ISSN: 0002-9939

Journal article

Burness TC, Liebeck MW, Shalev A, 2013, Generation and random generation: From simple groups to maximal subgroups, ADVANCES IN MATHEMATICS, Vol: 248, Pages: 59-95, ISSN: 0001-8708

Journal article

Jambor S, Liebeck MW, O'Brien EA, 2013, Some word maps that are non-surjective on infinitely many finite simple groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 45, Pages: 907-910, ISSN: 0024-6093

Journal article

Bamberg J, Giudici M, Liebeck MW, Praeger CE, Saxl Jet al., 2013, THE CLASSIFICATION OF ALMOST SIMPLE 3/2-TRANSITIVE GROUPS, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 365, Pages: 4257-4311, ISSN: 0002-9947

Journal article

Liebeck MW, 2013, Probabilistic and Asymptotic Aspects of Finite Simple Groups, PROBABILISTIC GROUP THEORY, COMBINATORICS, AND COMPUTING: LECTURES FROM THE FIFTH DE BRUN WORKSHOP, Editors: Detinko, Flannery, OBrien, Publisher: SPRINGER-VERLAG LONDON LTD, Pages: 1-34, ISBN: 978-1-4471-4813-5

Book chapter

Liebeck MW, Nikolov N, Shalev A, 2012, Product decompositions in finite simple groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 44, Pages: 469-472, ISSN: 0024-6093

Journal article

Liebeck MW, O'Brien EA, Shalev A, Pham HTet al., 2012, PRODUCTS OF SQUARES IN FINITE SIMPLE GROUPS, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 140, Pages: 21-33, ISSN: 0002-9939

Journal article

Liebeck MW, Seitz GM, 2012, Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, Publisher: American Mathematical Society., ISBN: 978-0-8218-6920-8

Book

Liebeck MW, Segal D, Shalev A, 2012, The density of representation degrees, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Vol: 14, Pages: 1519-1537, ISSN: 1435-9855

Journal article

Liebeck MW, O'Brien EA, Shalev A, Pham HTet al., 2011, Commutators in finite quasisimple groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 43, Pages: 1079-1092, ISSN: 0024-6093

Journal article

Liebeck MW, Shalev A, 2011, Fixed points of elements of linear groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 43, Pages: 897-900, ISSN: 0024-6093

Journal article

Liebeck MW, Nikolov N, Shalev A, 2011, Groups of Lie type as products of <i>SL</i><sub>2</sub> subgroups, JOURNAL OF ALGEBRA, Vol: 326, Pages: 201-207, ISSN: 0021-8693

Journal article

Liebeck MW, Litterick AJ, Marion C, 2011, A rigid triple of conjugacy classes in <i>G</i><sub>2</sub>, JOURNAL OF GROUP THEORY, Vol: 14, Pages: 31-35, ISSN: 1433-5883

Journal article

Liebeck MW, Macpherson D, Tent K, 2010, Primitive permutation groups of bounded orbital diameter, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 100, Pages: 216-248, ISSN: 0024-6115

Journal article

Liebeck MW, Praeger CE, Saxl J, 2010, Regular Subgroups of Primitive Permutation Groups, MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 203, Pages: 1-+, ISSN: 0065-9266

Journal article

Liebeck MW, O'Brien EA, Shalev A, Tiep PHet al., 2010, The Ore conjecture, JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, Vol: 12, Pages: 939-1008, ISSN: 1435-9855

Journal article

Liebeck MW, Nikolov N, Shalev A, 2010, A conjecture on product decompositions in simple groups, GROUPS GEOMETRY AND DYNAMICS, Vol: 4, Pages: 799-812, ISSN: 1661-7207

Journal article

Burness TC, Liebeck MW, Shalev A, 2009, Base sizes for simple groups and a conjecture of Cameron, PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, Vol: 98, Pages: 116-162, ISSN: 0024-6115

Journal article

Cargo DP, de Launey W, Liebeck MW, Stafford RMet al., 2008, Short two-variable identities for finite groups, JOURNAL OF GROUP THEORY, Vol: 11, Pages: 675-690, ISSN: 1433-5883

Journal article

Liebeck MW, Pyber L, Shalev A, 2007, On a conjecture of GE wall, JOURNAL OF ALGEBRA, Vol: 317, Pages: 184-197, ISSN: 0021-8693

Journal article

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