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.

**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

**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: