Open Research Online

Gill, Nick; Giudici, Michael and Spiga, Pablo (2024). A generalization of Szep's conjecture for almost simple groups. Vietnam Journal of Mathematics, 52 pp. 325–359.

Download Published Version (PDF / 566kB)

Hennig, Brett; Gill, Nick and Lord, Thomas (2024). Can we do inclusive politics in urgent times? Innovation: The European Journal of Social Science Research, 37(3) pp. 687–698.

Gill, Nick and Guillot, Pierre (2024). The binary actions of simple groups with a single conjugacy class of involutions. Journal of Group Theory (Early access).

Download Accepted Manuscript (PDF / 436kB)

Gill, Nick; Guillot, Pierre and Liebeck, Martin (2024). The binary actions of simple groups of Lie type of characteristic 2. Pacific Journal of Mathematics (In press).

Request a copy from the author This file is not available for public download

Gill, Nick and Liebeck, Martin W. (2023). Irredundant bases for finite groups of Lie type. Pacific Journal of Mathematics, 322(2) pp. 281–300.

Download Published Version (PDF / 401kB)

Garzoni, Daniele and Gill, Nick (2023). Large minimal invariable generating sets in the finite symmetric groups. Israel Journal of Mathematics, 255 pp. 581–598.

Download Submitted Manuscript (PDF / 210kB)

Garzoni, Daniele and Gill, Nick (2023). On the number of conjugacy classes of a primitive permutation group. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(1) pp. 115–136.

Download Published Version (PDF / 477kB)

Gill, Nick; Kimeu, Ngwava and Short, Ian (2022). Nilpotent covers of symmetric and alternating groups. Bulletin of the Belgian Mathematical Society – Simon Stevin, 29(2) pp. 249–266.

Request a copy from the author This file is not available for public download

Gill, N. and Lodà, B. (2022). Statistics for S_n acting on k-sets. Journal of Algebra, 607(Part A) pp. 286–299.

Gill, Nick; Liebeck, Martin W. and Spiga, Pablo (2022). Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups. Lecture Notes in Mathematics, 2302. Cham: Springer.

Gill, Nick and Hughes, Sam (2021). The character table of a sharply -transitive subgroup of the alternating group of degree 12. International Journal of Group Theory, 10(1) pp. 11–30.

Request a copy from the author This file is not available for public download

Gill, Nick; Lodá, Bianca and Spiga, Pablo (2021). On the height and relational complexity of a finite permutation group. Nagoya Mathematical Journal, 246 pp. 372–411.

Download Accepted Manuscript (PDF / 485kB)

Gill, N.; Pyber, L. and Szabó, E. (2020). A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank. Bulletin of the London Mathematical Society, 52(3) pp. 464–471.

Download Published Version (PDF / 157kB)

Gill, Nick and Spiga, Pablo (2020). Binary permutation groups: Alternating and classical groups. American Journal of Mathematics, 142(1) pp. 1–43.

Gill, Nick; Hunt, Francis and Spiga, Pablo (2019). Cherlin's conjecture for almost simple groups of Lie rank 1. Mathematical Proceedings of the Cambridge Philosophical Society, 167(3) pp. 417–435.

Gill, Nick; Gillespie, Neil I. and Semeraro, Jason (2018). Conway Groupoids and Completely Transitive Codes. Combinatorica, 38(2) pp. 399–442.

Download Accepted Manuscript (PDF / 564kB)

Dalla Volta, Francesca; Gill, Nick and Spiga, Pablo (2018). Cherlin’s conjecture for sporadic simple groups. Pacific Journal of Mathematics, 297(1) pp. 47–66.

Download Accepted Manuscript (PDF / 317kB)

Gill, Nick; Gillespie, Neil; Praeger, Cheryl and Semeraro, Jason (2017). Conway’s groupoid and its relatives. In: Bhargava, Manjul; Guralnick, Robert; Hiss, Gerhard; Lux, Klaus and Tiep, Pham Huu eds. Finite Simple Groups: Thirty Years of the Atlas and Beyond. Contemporary Mathematics, 694. American Mathematical Society, pp. 91–110.

Barrantes, Daniel; Gill, Nick and Ramírez, Jeremías (2016). Abelian covers of alternating groups. Archiv der Mathematik, 107(2) pp. 135–150.

Download Accepted Manuscript (PDF / 343kB)

Gill, Nick (2016). Quasirandom group actions. Forum of Mathematics, Sigma, 4, article no. e24.

Download Published Version (PDF / 486kB)

Gill, Nick (2016). Transitive projective planes and insoluble groups. Transactions of the American Mathematical Society, 368(5) pp. 3017–3057.

Download Accepted Manuscript (PDF / 492kB)

Gill, Nick; Gillespie, Neil I.; Nixon, Anthony and Semeraro, Jason (2016). Generating groups using hypergraphs. The Quarterly Journal of Mathematics, 67(1) pp. 29–52.

Download Accepted Manuscript (PDF / 378kB)

Britnell, John R. and Gill, Nick (2016). Perfect commuting graphs. Journal of Group Theory, 20(1)

Gill, Nick; Helfgott, Harald A. and Rudnev, Misha (2015). On growth in an abstract plane. Proceedings of the American Mathematical Society, 143(8) pp. 3593–3602.

Download Accepted Manuscript (PDF / 328kB)

Azad, Azizollah; Britnell, John R. and Gill, Nick (2015). Nilpotent covers and non-nilpotent subsets of finite groups of Lie type. Forum Mathematicum, 27(6)

Download Published Version (PDF / 464kB)

Gill, Nick and Helfgott, Harald Andrés (2014). Growth in solvable subgroups of GL_r(Z/pZ). Mathematische Annalen, 360(1-2) pp. 157–208.

Download Accepted Manuscript (PDF / 556kB)

Bamberg, John; Gill, Nick; Hayes, Thomas P.; Helfgott, Harald A.; Seress, Akos and Spiga, Pablo (2014). Bounds on the diameter of Cayley graphs of the symmetric group. Journal of Algebraic Combinatorics, 40(1) pp. 1–22.

Download Accepted Manuscript (PDF / 449kB)

Gill, Nick (2013). A note on the Weiss conjecture. Journal of the Australian Mathematical Society, 95(3) pp. 356–361.

Download Accepted Manuscript (PDF / 269kB)

Gill, Nick; Pyber, László; Short, Ian and Szabó, Endre (2013). On the product decomposition conjecture for finite simple groups. Groups, Geometry, and Dynamics, 7(4) pp. 867–882.

Download Accepted Manuscript (PDF / 324kB)

Gill, Nick (2013). Orientably regular maps with Euler characteristic divisible by few primes. Journal of the London Mathematical Society, 88(1) pp. 118–136.

Download Accepted Manuscript (PDF / 454kB)

Short, Ian and Gill, Nick (2013). Conjugacy in Thompson's group $F$ . Proceedings of the American Mathematical Society, 141 pp. 1529–1538.

Download Accepted Manuscript (PDF / 116kB)

Gill, Nick (2013). (2,m,n)-groups with Euler characteristic equal to $-2^as^b$ . Electronic Journal of Combinatorics, 20(3), article no. 8.

Download Accepted Manuscript (PDF / 420kB)

Gill, Nick and Singh, Anupam (2011). Real and strongly real classes in SL_n(q). Journal of Group Theory, 14(3) pp. 437–459.

Download Published Version (PDF / 211kB)

Gill, Nick and Singh, Anupam (2011). Real and strongly real classes in PGL_n(q) and quasi-simple covers of PSL_n(q). Journal of Group Theory, 14(3) pp. 461–489.

Download Published Version (PDF / 243kB)

Gill, Nick and Helfgott, Harald Andres (2011). Growth of small generating sets in SL_n(ℤ/pℤ). International Mathematics Research Notices, 18 pp. 4226–4251.

Gill, Nick and Short, Ian (2010). Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line. Aequationes Mathematicae, 79(1-2) pp. 23–37.

Download Accepted Manuscript (PDF / 183kB)

Gill, Nick; O'Farrell, Anthony G. and Short, Ian (2009). Reversibility in the group of homeomorphisms of the circle. Bulletin of the London Mathematical Society, 41(5) pp. 885–897.

Download Accepted Manuscript (PDF / 229kB)

Camina, Alan R.; Gill, Nick and Zalesski, A. E. (2008). Large dimensional classical groups and linear spaces. Bulletin of the Belgian Mathematical Society (Simon Stevin), 15(4) pp. 705–731.