Martin W. Liebeck
Research Papers


Electronic Preprints

Here’s a selection of papers published since 2003.

Clicking on the title of a paper will take you to a page from which you can download the paper in at least one format.

 

            Applications of character theory of finite simple groups

           (chapter in EMS Lecture Notes Series, to appear)

 

           The depth of a finite simple group

           (with T. Burness and A. Shalev), Proc. Amer. Math. Soc, to appear

 

           Generation of second maximal subgroups and the existence of      special primes

           (with T. Burness and A. Shalev), Forum Math. Sigma, to appear

 

           Chiral maps and finite simple groups

           (with D. Leemans), Bull. London Math. Soc., to appear

 

           Finite subgroups of simple algebraic groups with irreducible centralizers

            (with A. Thomas), J. Group Theory 20 (2017), 841-870.

 

               Unipotent class representatives for finite classical groups

            (with S. Gonshaw and E.A. O’Brien), J. Group Theory 20 (2017), 505-525.

       

               3/2-transitive permutation groups and ½-transitive linear groups

            (with C.E. Praeger and J. Saxl), Proc. Amer. Math. Soc., to appear

 

               Character ratios for finite groups of Lie type, and applications

            Contemporary Mathematics 694 (2017), American Math. Soc., 193-208.

               Rapid growth in finite simple groups

            (with G. Schul and A. Shalev), Trans. Amer. Math. Soc. 369     (2017), 8765-8779.  

 

            Recognition of finite exceptional groups of Lie type

            (with E. O’Brien), Trans. Amer. Math. Soc. 368 (2016), 6189-6226

 

                Arithmetic results on orbits of linear groups

            (with M. Giudici, C.E. Praeger, J. Saxl and P.H. Tiep), Trans. Amer. Math. Soc. 368 (2016), 2415-2467

 

               Distinguished unipotent elements and multiplicity-free subgroups of simple algebraic groups

 

            (with G.M. Seitz and D.M. Testerman), Pacific J. Math. 279 (2015), 357-382

 

            Width questions for finite simple groups

            Groups St. Andrews 2013, London Math. Soc. Lecture Note Series, Cambridge Univ. Press, 2015

 

            On products of involutions in finite groups of Lie type in even characteristic

             J. Algebra 421 (2015), 431-437

 

             On fixed points of elements in primitive permutation groups

               

             (with A. Shalev), J. Algebra 421 (2015), 438-459

 

                Outer unipotent classes in automorphism groups of simple algebraic groups

             (with R. Lawther and G. Seitz), Proc. London Math. Soc. 109 (2014), 553-595

               

                  Bases of primitive linear groups II

                (with A. Shalev), J. Algebra 403 (2014), 223-228

 

                Generation and random generation: from simple groups to maximal subgroups

               (with T. Burness and A. Shalev), Advances Math. 248 (2013), 59-95.

 

               Power sets and soluble subgroups

              (with A. Shalev), Proc. Amer. Math. Soc. 142 (2014), 3757-3760.

 

                Probabilistic and asymptotic aspects of finite simple groups

             in Probabilistic group theory, combinatorics and computing, Springer Lecture Notes in Math. 2070 (2013), pp. 1-34.

 

                Some word maps that are non-surjective on infinitely many finite simple groups

 

                    (with S. Jambor and E. O'Brien), Bulletin London Math. Soc. 45 (2013), 907-910

 

                Powers in finite groups and a criterion for solubility

 

                (with A. Shalev), Proc. Amer. Math. Soc. 141 (2013), 4179-4189

 

               The classification of almost simple 3/2-transitive groups

                (with J. Bamberg, M. Giudici, C. Praeger and J. Saxl), Transactions Amer. Math. Soc. 365 (2013), 4257-4311

 

               Product decompositions in finite simple groups

               (with N. Nikolov, A. Shalev), Bulletin London Math. Soc. 44 (2012), 469-472

 

               The density of representation degrees

               (with A. Shalev and D. Segal), J. European Math. Soc. 14 (2012), 1519-1537

 

               Commutators in finite quasisimple groups

               (with E. O'Brien, A. Shalev, P. Tiep), Bulletin London Math. Soc. 43 (2011), 1079-1092

 

               Fixed points of elements of linear groups

               (with A. Shalev), Bulletin London Math. Soc. 43 (2011), 897-900

 

               Products of squares in finite simple groups

               (with E. O'Brien, A. Shalev, P. Tiep), Proc. Amer. Math. Soc. 140 (2012), 21-33

 

               A rigid triple of conjugacy classes in G_2

               (with A. Litterick and C. Marion), J. Group Theory 14 (2011), 31--36              

 

              Groups of Lie type as products of SL_2 subgroups

 

              (with N. Nikolov, A. Shalev), J. Algebra 326 (2011), 201-207

 

               A conjecture on product decompositions in simple groups

              (with N. Nikolov and A. Shalev), Groups, Geometry and Dynamics 4 (2010), 799-–812

 

         

              The Ore Conjecture

 

              (with E. O'Brien, A. Shalev, P. Tiep), J. European Math. Soc. 12 (2010), 939 - 1008

 

 

              On regular subgroups of primitive permutation groups

 

              (with C. Praeger and J. Saxl),  Memoirs Amer. Math. Soc. 203 (2010), No. 952, pp. 1-88

 

 

              Primitive permutation groups of bounded orbital diameter

 

              (with H.D. Macpherson and K. Tent), Proc. London Math. Soc. 100 (2010), 216-248

 

           

             Base sizes for simple groups and a conjecture of Cameron

 

            (with T. Burness and A. Shalev), Proc. London Math. Soc. 98 (2009), 116-162

 

           

             Short Two-Variable Identities for Finite Groups

 

             (with D. Cargo. W. de Launey and R. Stafford), J. Group Theory 11 (2008), 675-690

 

 

             The sparsity of dimensions of irreducible representations of finite simple groups

 

             (with A. Shalev), Bull. London Math. Soc. 39 (2007), 467-472

 

 

             Finding the characteristic of a group of Lie type

 

             (with E. O'Brien), J. London Math. Soc. 75 (2007), 741-754

 

 

             On a conjecture of G.E. Wall

 

             (with A. Shalev), J. Algebra 317 (2007), 184-197

 

     Fuchsian groups, finite simple groups and representation varieties

     (with Aner Shalev), Inventiones Math. 159 (2005), 317-367

 

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

(with Ben Martin and Aner Shalev), Duke Math. J. 128 (2005), 541-557

 

     Character degrees and random walks in finite groups of Lie type

(with Aner Shalev), Proc. London Math. Soc. 90 (2005), 61-86

 

     Maximal subgroups of large rank in exceptional groups of Lie type

(with Gary Seitz), J. London Math. Soc. 71 (2005), 345-361

 

     Irreducible subgroups of algebraic groups

(with Donna Testerman), Quarterly J. Math 55 (2004), 47-55

 

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

(with Gary Seitz), J. Group Theory 7 (2004), no. 3, 347-372

 

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

(with Aner Shalev), J. Algebra 276 (2004), 552-601.

 

     The maximal subgroups of positive dimension in exceptional algebraic groups

(with Gary Seitz), Memoirs Amer. Math. Soc. 169 (2004), no. 802, vi+227 pp.

 

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

(with Aner Shalev), Communications in Algebra 32 (2004), 657-661

 

     Residual properties of the modular group and other free products

(with Aner Shalev), J. Algebra 268 (2003), 264-285

 

     Residual properties of free products of finite groups

(with Aner Shalev), J. Algebra 268 (2003), 286-289

 

     Variations on a theme of Steinberg

(with Gary Seitz), J. Algebra 260 (2003), 261-297

 

     A survey of maximal subgroups of exceptional groups of Lie type

(with Gary Seitz), in Groups, Combinatorics and Geometry: Durham, 2001, World Scientific, 2003

 

     Bases of primitive permutation groups

(with Aner Shalev), in Groups, Combinatorics and Geometry: Durham, 2001, World Scientific, 2003