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.
Zero-one generation laws for
finite simple groups
(with R. Guralnick,
F. Luebeck and A. Shalev),
Proc. American Math. Soc., to appear
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 paqb 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: