Research Papers

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.

**Character bounds for finite
groups of Lie type**

(with R. Bezrukavnikov, A. Shalev
and P. Tiep),

Acta Math., to appear

__Surjective word maps and
Burnside's p ^{a}q^{b} theorem__

(with R. Guralnick, E.
O’Brien, A. Shalev and P. Tiep),

Inventiones Math., to appear

__Bases for quasisimple linear
groups __

(with M. Lee), Algebra and Number Theory, to appear

__The length and depth of
algebraic groups__

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

__Permutation Representations of
Nonsplit Extensions involving
Alternating Groups
__

(with R. Guralnick), Israel J.
Math., to appear

**Applications of character theory of finite
simple groups**

**
**(chapter in EMS Lecture Notes
Series, 2018)

**The depth of a finite simple group**

**
**(with T. Burness and A.
Shalev), Proc. Amer. Math. Soc, 146 (2018), 2343-2358

**Generation of second maximal subgroups
and the existence of special primes
**

**
**(with T. Burness and A.
Shalev), Forum Math. Sigma 5 (2017), e25, 41 pp

**Chiral maps and finite simple
groups**

**
**(with D. Leemans), Bull.
London Math. Soc. 49 (2017), 581-592

**
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

**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

**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

**Fixed points
of elements of linear groups**

(with A. Shalev), Bulletin

**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

**
A conjecture on
product decompositions in simple groups**

(with

(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.

**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.

**
Finding the characteristic of a group of Lie
type**

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

(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:

** Bases of primitive permutation groups **

(with Aner Shalev), in
Groups, Combinatorics and Geometry: