Emeritus Professor of Mathematics, University of Oxford
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
ON THE LINEARITY OF TORSION-FREE NILPOTENT GROUPS OF FINITE MORLEY RANK
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY issue 5 volume 137 page 1813-1821 (2009) Full text available
The probability of generating a nilpotent subgroup of a finite group
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY volume 40 page 568-580 (August 2008) Full text available
The probability of generating a soluble subgroup of a finite group
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES volume 75 page 431-446 (April 2007) Full text available
Free product decompositions in images of certain free products of groups
JOURNAL OF ALGEBRA issue 1 volume 310 page 57-69 (1 April 2007) Full text available
Finite axiomatization of finite soluble groups
Journal of the London Mathematical Society issue 3 volume 74 page 566-582 (December 2006)
profinite groups, finite and infinite soluble groups, model theory of groups, branch groups, word growth of groups, finitely presented groups, generation problems for finite simple groups.
Major / recent publications:
Profinite groups. London Math. Soc. Monographs, New Series 19 (Clarendon Press, Oxford, 1998).
(with R.M. Guralnick) On the probability of generating a finite soluble group. Proc. London Math. Soc. (3) 81 (2000), 405-427.
(with R.I. Grigorchuk) A structural property concerning abstract commensurability of subgroups. J. London Math. Soc. (2) 68 (2003), 671-682.
On exponential growth and uniformly exponential growth for groups. Invent. Math. 155 (2004), 287-303.
On growth of groups with few relators. Bull. London Math. Soc. 36 (2004), 1-2.
(with J.N. Bray and R.A. Wilson) A characterization of finite soluble groups by laws in two variables. Bull. London Math. Soc. 37 (2005), 179-186.
Finite axiomatization of finite soluble groups. J. London Math. Soc. (2) 74 (2006), 566-582.
Structure theory for branch groups. In Geometric and Homological Topics in Group Theory (Cambridge University Press, 2009), 306-320.
First-order characterization of the radical of a finite group. J. Symbolic Logic 74 (2009), 1429-1435.
Large hereditarily just infinite groups. J. Algebra 324 (2010), 248-255.
Characterization of the soluble radical by a sequence of words. J. Algebra 326 (2011), 286-289.
Finite index subgroups and verbal subgroups in profinite groups. Astérisque 339 (2011), 387-408.
The gap in the growth of residually soluble groups. Bull. London Math. Soc. 43 (2011), 576-582.
(with J.R.J. Groves) Soluble groups with a finiteness condition arising from Bredon cohomology. Bull. London Math. Soc. 45 (2013), 89-92.
(with A. Garrido) On subgroups of finite index in branch groups. J. Algebra 397 (2014), 32-38.
(with A. Thom) Metric ultraproducts of finite simple groups. C. R. Math. Acad. Sci. Paris 352 (2014), 463-466.
(with I.M. Chiswell and A.M.W. Glass) Residual nilpotence and ordering in one-relator groups and knot groups. Math. Proc. Cambridge Philos. Soc. 158 (2015), 275-288.
The first-order theory of branch groups. J. Austral. Math. Soc. 102 (2017), 150-158.
(with A.M.W. Glass) Recognising the real line. To appear.
Popular article. The glass bead game. Math. Intelligencer 19 (1997), no. 2, 23--25.