Imperial College London

ProfessorMartinLiebeck

Faculty of Natural SciencesDepartment of Mathematics

Head of the Pure Mathematics Section
 
 
 
//

Contact

 

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

 
 
//

Location

 

665Huxley BuildingSouth Kensington Campus

//

Summary

 

Publications

Publication Type
Year
to

127 results found

Burness TC, Liebeck MW, Shalev A, The depth of a finite simple group, Proceedings of the American Mathematical Society, ISSN: 0002-9939

We introduce the notion of the depth of a finite group G, defined as theminimal length of an unrefinable chain of subgroups from G to the trivial subgroup. Inthis paper we investigate the depth of (non-abelian) finite simple groups. We determinethe simple groups of minimal depth, and show, somewhat surprisingly, that alternatinggroups have bounded depth. We also establish general upper bounds on the depth ofsimple groups of Lie type, and study the relation between the depth and the much studiednotion of the length of simple groups. The proofs of our main theorems depend (amongother tools) on a deep number-theoretic result, namely, Helfgott’s recent solution of theternary Goldbach conjecture.

JOURNAL ARTICLE

Liebeck MW, Burness TC, Shalev A, Generation of second maximal subgroups and the existence of special primes, Forum of Mathematics, Sigma, ISSN: 2050-5094

JOURNAL ARTICLE

Liebeck MW, Praeger CE, Saxl J, The classification of 3/2-transitive permutation groups and 1/2-transitive linear groups, Proceedings of the American Mathematical Society, ISSN: 1088-6826

A linear group G ≤ GL(V ), where V is a finite vector space, is called 12-transitive if allthe G-orbits on the set of nonzero vectors have the same size. We complete the classificationof all the 12-transitive linear groups. As a consequence we complete the determination of thefinite 32-transitive permutation groups – the transitive groups for which a point-stabilizerhas all its nontrivial orbits of the same size. We also determine the (k +12)-transitive groupsfor integers k ≥ 2.

JOURNAL ARTICLE

Liebeck MW, Schul G, Shalev A, Rapid growth in finite simple groups, Transactions of the American Mathematical Society, ISSN: 1088-6850

We show that small normal subsets A of finite simple groups growvery rapidly – namely, |A2| ≥ |A|2− , where > 0 is arbitrarily small.Extensions, consequences, and a rapid growth result for simple algebraicgroups are also given.

JOURNAL ARTICLE

Gonshaw S, Liebeck MW, O'Brien EA, 2017, Unipotent class representatives for finite classical groups, JOURNAL OF GROUP THEORY, Vol: 20, Pages: 505-525, ISSN: 1433-5883

JOURNAL ARTICLE

Leemans D, Liebeck MW, 2017, Chiral polyhedra and finite simple groups, BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, Vol: 49, Pages: 581-592, ISSN: 0024-6093

JOURNAL ARTICLE

Liebeck MW, 2017, Character ratios for finite groups of Lie type, and applications, FINITE SIMPLE GROUPS: THIRTY YEARS OF THE ATLAS AND BEYOND, Vol: 694, Pages: 193-208, ISSN: 0271-4132

JOURNAL ARTICLE

Liebeck MW, Thomas AR, 2017, Finite subgroups of simple algebraic groups with irreducible centralizers, JOURNAL OF GROUP THEORY, Vol: 20, Pages: 841-870, ISSN: 1433-5883

JOURNAL ARTICLE

Giudici M, Liebeck MW, Praeger CE, Saxl J, Pham HTet al., 2016, ARITHMETIC RESULTS ON ORBITS OF LINEAR GROUPS, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 368, Pages: 2415-2467, ISSN: 0002-9947

JOURNAL ARTICLE

Liebeck MW, O'Brien EA, 2016, RECOGNITION OF FINITE EXCEPTIONAL GROUPS OF LIE TYPE, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 368, Pages: 6189-6226, ISSN: 0002-9947

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, 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

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

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

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

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

Liebeck MW, 2013, Probabilistic and Asymptotic Aspects of Finite Simple Groups, Editors: Detinko, Flannery, OBrien, Publisher: SPRINGER-VERLAG LONDON LTD, Pages: 1-34, ISBN: 978-1-4471-4813-5

BOOK CHAPTER

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

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, 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, 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, Litterick AJ, Marion C, 2011, A rigid triple of conjugacy classes in G(2), JOURNAL OF GROUP THEORY, Vol: 14, Pages: 31-35, ISSN: 1433-5883

JOURNAL ARTICLE

Liebeck MW, Nikolov N, Shalev A, 2011, Groups of Lie type as products of SL2 subgroups, JOURNAL OF ALGEBRA, Vol: 326, Pages: 201-207, ISSN: 0021-8693

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, 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

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.

Request URL: http://wlsprd.imperial.ac.uk:80/respub/WEB-INF/jsp/search-html.jsp Request URI: /respub/WEB-INF/jsp/search-html.jsp Query String: respub-action=search.html&id=00003537&limit=30&person=true