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Nick Gill known as Nick Gill


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BSc(Hons), PhD (Cantab)


I did my undergraduate studies in Australia, my PhD in England. I have held postdocs in Ghent (Belgium), Chennai (India), Bristol (UK) and the Open University (UK). In 2014 I was a visiting professor at the Universidad de Costa Rica. In Jan 2015 I started work as a lecturer at USW.


An up-to-date list of my publications can be found on my website; the list below includes all papers accepted for publication as of January 2015.

  1. (with Azizollah Azad and John Britnell). Nilpotent covers and non-nilpotent subsets of finite groups of Lie type, to appear in Forum Mathematicum.
  2. (with Laszlo Pyber, Ian Short and Endre Szabo). On the product decomposition conjecture for finite simple groups. Groups, Geometry, and Dynamics, 7 (2013), no.4, 867–882.
  3. Orientably regular maps with Euler characteristic divisible by few primes. Journal of the London Mathematical Society, 88 (2013), no.1, 118–136.
  4. (with Ian Short). Conjugacy in Thompson’s group F. Proceedings of the American Mathematical Society, 141 (2013)1529–1538.
  5. Transitive projective planes and insoluble groups. Transactions of the American Mathematical Society (2013, in press).
  6. (with Harald Helfgott and Misha Rudnev). On growth in an abstract plane. Proceedings of the American Mathematical Society (2013, in press).
  7. (2,m,n)-groups with Euler characteristic equal to −2asb. Electronic Journal of Combinatorics, 20 (2013), no. 3, R8.
  8. A note on the Weiss conjecture. Journal of the Australian Mathematical Society (2013, in press).
  9. (with John Bamberg, Thomas P. Hayes, Harald Helfgott, Akos Seress and Pablo Spiga). Bounds on the diameter of Cayley graphs of the symmetric group. Journal of Algebraic Combinatorics (2013, in press).
  10. (with Anupam Singh). Real and strongly real classes in SLn(q). Journal of Group Theory, 14 (2011), no.3, pp. 437–459.
  11. (with Anupam Singh) Real and strongly real classes in PGLn(q) and quasi-simple covers of PSLn(q). Journal of Group Theory, 14 (2011), no.3, 461–489.
  12. (with Harald Helfgott) Growth of small generating sets in SLn(ℤ/pℤ). International Mathematics Research Notices, 18 (2011), 4226–4251.
  13. (with Ian Short) Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Mathematicae, 79(2010), no.1-2, 23–37.
  14. (with Anthony G. O’Farrell and Ian Short) Reversibility in the group of homeomorphisms of the circle. Bulletin of the London Mathematical Society, 41 (2009), no.5, 885–897.
  15. (with Alan Camina and Alex Zalesski) Large dimensional classical groups and linear spaces. Bulletin of the Belgian Mathematical Society (Simon Stevin), 15 (2008), no.4, 705–731.
  16. Transitive projective planes. Advances in Geometry, 7 (2007), no.4, 475–528.
  17. PSL and line-transitive linear spaces. Beiträge zur Algebra und Geometrie, 48 (2007), no.2, 591–620.
  18. Polar spaces and embeddings of classical groups. New Zealand Journal of Mathematics, 36 (2007), 175–184.
  19. Linear spaces with significant characteristic prime. Innovations in Incidence Geometry, 3 (2006), 109–119.
  20. Nilpotent Singer groups. Electronic Journal of Combinatorics, 13 (2006), no.1, R94.


My research is in group theory, a branch of algebra. Put another way, group theory is the mathematical study of symmetry; my main focus is on finite groups.

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