Preprints of my (recent) papers are on the arXiv

Publications (and submitted/accepted papers)

  1. S.P. Glasby, Alice C. Niemeyer, and Cheryl E. Praeger, The probability that two elements with large 1-eigenspaces generate a classical group, arXiv

  2. S.P. Glasby, Hilbert’s Theorem 90, periodicity, and roots of Artin-Schreier polynomials arXiv

  3. S.P. Glasby, Classifying finite groups G with three Aut(G)-orbits, Ischia Group Theory 2024 (IGT 2024), XX(2025), XX-XX. | arXiv

  4. S.P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger and A. E. Zalesski, Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime, J. Algebra XX(202X), XX-XX. DOI | arXiv

  5. S.P. Glasby and Alexander Bors, Finite 2-groups with exactly three automorphism orbits, J. Group Theory 28 (2025), 1335–1359. DOI | arXiv

  6. S.P. Glasby, Mathematics of the NYT daily word game Waffle, arXiv | Magma code

  7. S.P. Glasby, Alice C. Niemeyer and Cheryl E. Praeger, Bipartite q-Kneser graphs and two-generated irreducible linear groups, Linear Algebra Appl. 710 (2025), 203–229. DOI | arXiv

  8. S.P. Glasby and G.R. Paseman, Maximizing weighted sums of binomial coefficients using generalized continued fractions, Proc. R. Soc. Edinb. 59(1) (2024), 1–22. DOI | arXiv | Magma code

  9. Vishnuram Arumugam, Heiko Dietrich and S.P. Glasby, Derangements in wreath products of permutation groups, J. Algebraic Combin. 59 (2024), 1–22. arXiv | DOI

  10. S.P. Glasby, Ferdinand Ihringer and Sam Mattheus, The proportion of non-degenerate complementary subspaces in classical spaces, Des. Codes, Cryptogr. 91(9) (2023), 2879–2891. arXiv | GAP FinIng code | DOI

  11. Gordon F. Royle, Cheryl E. Praeger, S.P. Glasby, Saul D. Freedman and Alice Devillers, Tournaments and even graphs are equinumerous, J. Algebraic Combin. 57 (2023), 515–524. arXiv | DOI

  12. Michael Giudici, S.P. Glasby and Cheryl E. Praeger, Subgroups of classical groups that are transitive on subspaces, J. Algebra 636 (2023), 804–868. arXiv | DOI

  13. S.P. Glasby, Alice C. Niemeyer and Cheryl E. Praeger, Random generation of direct sums of finite non-degenerate subspaces, Linear Algebra Appl. 649 (2022), 408–432. arXiv | DOI

  14. S.P. Glasby, Alice C. Niemeyer and Cheryl E. Praeger, The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension, Finite Fields Their Appl. 82 (2022), paper no. 102055. arXiv | DOI

  15. Faezeh Alizadeh, S.P. Glasby and Cheryl E. Praeger, Sequences of linear codes where the rate times distance grows rapidly, J. Algebra Comb. Discrete Struct. Appl. 10(2) (2022), 105–113. arXiv

  16. S.P. Glasby and G.R. Paseman, On the maximum of the weighted binomial sum $2^{-r}\sum_{i=0}^r\binom{m}{i}$, Electron. J. Combin. 29(2) (2022), article P2.5. arXiv | DOI

  17. Dominik Bernhardt, Tim Boykett, Alice Devillers, Johannes Flake and S.P. Glasby, The groups G satisfying a functional equation f(xk) = xf(x) for some k ∈ G, J. Group Theory 25(6) (2022), 1055–1081. arXiv | DOI paper | Magma code | DOI Magma code

  18. S.P. Glasby, Cheryl E. Praeger, and W.R. Unger, Most permutations power to a cycle of small prime length, Proc. R. Soc. Edinb. 64(2) (2021), 234–246. arXiv | DOI

  19. S.P. Glasby, E. Pierro and Cheryl E. Praeger, Point-primitive generalised hexagons and octagons and projective linear groups, Ars Math. Contemp. 21 (2021), #P2.10. arXiv | DOI

  20. Mariagrazia Bianchi, S.P. Glasby and Cheryl E. Praeger, Conjugacy class sizes in arithmetic progression J. Group Theory 23(6) (2020), 1039–1056. pdf | arXiv | DOI

  21. S.P. Glasby, Cheryl E. Praeger and Colva M. Roney-Dougal, Involution centralisers in finite unitary groups of odd characteristic J. Algebra 545 (2020), 245–299. arXiv

  22. John Bamberg, S.P. Glasby, Scott Harper and Cheryl E. Praeger, Permutations with orders coprime to a given integer, Electron. J. Combin. 27(1) (2020), #P1.6. arXiv | Magma code | DOI

  23. S.P. Glasby, Classifying uniformly generated groups, Commun. Algebra 48 (2020), 101–104. arXiv | DOI

  24. Alice Devillers and S.P. Glasby, Roots of unity and unreasonable differentiation, Archiv der Mathematik 113(4) (2019), 367–371. arXiv | DOI

  25. John Bamberg, S.P. Glasby, Luke Morgan and Alice C. Niemeyer, Corrigendum: Maximal linear groups induced on the Frattini quotient of a p-group, J. Pure Appl. Algebra 223 (2019), no. 12, 5428–5429. DOI

  26. S.P. Glasby, Frederico A. M. Ribeiro and Csaba Schneider, Duality between p-groups with three characteristic subgroups and semisimple anti-commutative algebras, Proc. R. Soc. Edinb. 150(4) (2019), 1827–1852. arXiv | DOI

  27. S.P. Glasby, Cyclotomic ordering Conjecture arXiv (2019) solution by Pomerance and Rubinstein-Salzedo.

  28. S.P. Glasby, Alice C. Niemeyer and Tomasz Popiel, On the second-largest Sylow subgroup of a finite simple group of Lie type, Bull. Austral. Math. Soc. 99 (2019), 203–211. arXiv | Magma code | DOI

  29. Michael Giudici, S.P. Glasby, Cai Heng Li and Gabriel Verret, Arc-transitive digraphs with quasiprimitive local actions, J. Pure Appl. Algebra 223 (2019), 1217-1226. arXiv | Doi

  30. S.P. Glasby, Cheryl E. Praeger and Binzhou Xia, `Norman involutions’ and tensor products of unipotent Jordan blocks Israel J. Math. 230(1) (2019), 153–181. arXiv | Magma code | DOI

  31. S.P. Glasby and Cheryl E. Praeger, On the parameters of intertwining codes, Ars Math. Contemp. 16 (2019), 49–58. arXiv | DOI

  32. John Bamberg, S.P. Glasby, Luke Morgan and Alice C. Niemeyer, Maximal linear groups induced on the Frattini quotient of a p-group J. Pure Appl. Algebra 222 (2018), 2931–2951. arXiv | DOI | Magma code: associative & commutator laws

  33. S.P. Glasby, Cheryl E. Praeger, Kyle Rosa and Gabriel Verret, Bounding the composition length of primitive permutation groups and completely reducible linear groups, J. London Math. Soc 98(2) (2018), 557–572. arXiv | DOI

  34. Michael Giudici, S.P. Glasby, Cai Heng Li and Gabriel Verret, The number of composition factors of order p in completely reducible groups of characteristic p, J. Algebra 490 (2017), 241–255. arXiv | DOI

  35. Adel Alahmadi, S.P. Glasby and Cheryl E. Praeger, On the dimension of twisted centralizer codes, Finite Fields Appl. 48 (2017), 43–59. arXiv | DOI

  36. Adel Alahmadi, S.P. Glasby, Cheryl E. Praeger, Patrick Solé, Bahattin Yildiz, Twisted Centralizer Codes, Linear Algebra Appl. 524 (2017), 235–249. arXiv | [DOI](https:doi.org/10.1016/j.laa.2017.03.011} | Magma code

  37. Managing Editor: J. Austral. Math. Soc. 102(1) (2017), 1–161. Special issue dedicated to the memory of L.G. Kovács. Editors: Dane Flannery, Cheryl E. Praeger, Ralph Stöhr. Table of contents for Volume 102, Issue 1.

  38. Editorial to this special issue in memory of Laci Kovács (with Dane Flannery, Cheryl E. Praeger, Ralph Stöhr), J. Austral. Math. Soc. 102(1) (2017), 1–2. DOI

  39. S.P. Glasby, Frank Lübeck, Alice C. Niemeyer, Cheryl E. Praeger, Primitive prime divisors and the n-th cyclotomic polynomial, J. Austral. Math. Soc. 102 (2017), 122–135. arXiv | DOI | Magma code | GAP code

  40. John Bamberg, S.P. Glasby, Tomasz Popiel, Csaba Schneider, Point-primitive generalised hexagons and octagons, J. Combin. Theory Ser. A 147 (2017), 186–204. arXiv | DOI | AI podcast

  41. S.P. Glasby, Cheryl E. Praeger, Binzhou Xia, Decomposing modular tensor products, and periodicity of `Jordan partitions’ J. Algebra 450 (2016), 570–587. arXiv | DOI

  42. John Bamberg, S.P. Glasby and Eric Swartz, AS-configurations and skew-translation generalised quadrangles, J. Algebra 421 (2015), 311–330. arXiv | DOI

  43. S.P. Glasby, Cheryl E. Praeger, Binzhou Xia, Decomposing modular tensor products: `Jordan partitions’, their parts and p-parts, Israel J. Math. 209(1) (2015), 215–233. arXiv | DOI

  44. John Bamberg, S.P. Glasby, Tomasz Popiel and Cheryl E. Praeger, Generalised quadrangles and transitive pseudo-hyperovals, J. Comb. Des. 24(4) (2014), 151–164. arXiv | DOI

  45. S.P. Glasby, Distant parents in complete binary trees, Math. Scientist 38(1) (2013), 1–10. arXiv | DOI

  46. Scott Brown, Michael Giudici, S.P. Glasby, and Cheryl E. Praeger, Proportion of cyclic matrices in maximal reducible matrix algebras, J. Algebra 369 (2012), 360–368. arXiv | DOI

  47. S.P. Glasby, P.P. Pálfy and Csaba Schneider, p-groups having a unique proper nontrivial characteristic subgroup, J. Algebra 348 (2011), 85–109. arXiv | DOI

  48. S.P. Glasby, Enumerating the rationals from left to right, Amer. Math. Monthly 118 (2011), 830–835. arXiv | DOI

  49. S.P. Glasby and Cheryl E. Praeger, Towards an efficient Meat-axe algorithm using f-cyclic matrices: the density of uncyclic matrices in M(n,q), J. Algebra 322 (2009), 766–790. pdf | DOI | Appendix 1 The polynomials unc(n,q) for n ≤ 37. Appendix 2 Magma computer programs for verifying Conjecture 3 for small n.
    PhD thesis Sophie Ambrose, School of Mathematics and Statistics, University of Western Australia, 2006.

  50. C.J.Glasby, S.P. Glasby and F. Pleijel, Worms by number, Proc. Royal Soc. B 295 (2008), 2071–2076. pdf | ProcRoyalSocBpdf | DOI

  51. S.P. Glasby, Writing representations over proper division subrings, J. Algebra 319 (2008), 77–92. arXiv | DOI

  52. S.P. Glasby, The shape of solvable groups with odd order, in: Groups St Andrews 2005, vol. 2, Edited by C.M. Campbell, M.R. Quick, E.F. Robertson and G.C. Smith, London Mathematical Society Lecture Notes Series 340, Cambridge Univ. Press, (2007), 432–437. arXiv | DOI

  53. S.P. Glasby, The Meat-axe and f-cyclic matrices J. Algebra 300 (2006), 77–90. pdf | DOI

  54. S.P. Glasby, C.R. Leedham-Green, and E.A. O’Brien, Writing projective representations over proper subfields, J. Algebra 295 (2006), 51–61. pdf | DOI

  55. S.P. Glasby, Solvable groups with a given solvable length, and minimal composition length, J. Group Theory 8 (2005), 339–350. pdf | arXiv | DOI

  56. S.P. Glasby, Modules induced from a normal subgroup of prime index, in Rings, Modules, and Abelian Groups, Eds. A. Facchini, E. Houston and L. Salce, Lecture Notes in Pure and Applied Mathematics 236 (2004), 257–270. pdf | [DOI(https://doi.org/10.1201/9780824750817)

  57. S.P. Glasby, On the tensor product of polynomials over a ring, J. Austral. Math. Soc. 71 (2001), 1–17. DOI | pdf

  58. S.P. Glasby, Using recurrence relations to count certain elements in symmetric groups, European J. Combin. 22 (2001), 497–501. arXiv | DOI

  59. S.P. Glasby, Extended Euclid’s algorithm via backward recurrence relations, Math. Mag. 75 (1999), 228–230. DOI

  60. S.P. Glasby, Subgroups of the upper-triangular matrix group with maximal derived length and a minimal number of generators, in Groups St Andrews 1997 in Bath, I, Edited by C.M. Campbell et al., London Mathematical Society Lecture Notes Series 260, Cambridge Univ. Press, (1999), 275–281. pdf | arXiv | DOI

  61. S.P. Glasby and R.B. Howlett, Writing representations over minimal fields, Comm. Algebra 25 (1997), 1703–1712. pdf | DOI

  62. S.P. Glasby and L.G. Kovács, Irreducible modules and normal subgroups of prime index, Comm. Algebra 24 (1996), 1529–1546. pdf | WallKovacs | DOI

  63. S.P. Glasby, On generators for the group of units of the ring of integers modulo n, Austral. Math. Soc. Gaz. 22 (1995), 226–228. pdf

  64. S.P. Glasby, On the faithful representations, of degree 2n, of certain extensions of 2-groups by orthogonal or symplectic groups, J. Austral. Math. Soc. Ser. A 58 (1995), 232–247. DOI

  65. S.P. Glasby and R.B. Howlett, Extraspecial towers and Weil representations, J. Algebra 151 (1992), 236–260. DOI

  66. S.P. Glasby and M.C. Slattery, Computing intersections and normalizers in soluble groups, J. Symbolic Comput. 9 (1990), 637–651. DOI

  67. S.P. Glasby, The composition and derived lengths of a finite soluble group, J. Algebra 120 (1989), 406–413. DOI

  68. S.P. Glasby, Computational approaches to the theory of finite soluble groups. Bull. Austral. Math. Soc. 38 (1988), 157–158. DOI

  69. S.P. Glasby, Constructing normalisers in finite soluble groups, J. Symolic Comput. 5 (1988), 285–294. DOI

  70. S.P. Glasby, Intersecting subgroups of finite soluble groups. J. Symbolic Comput. 5 (1988), 295–301. DOI

  71. S.P. Glasby, 2-groups with every automorphism central. J. Austral. Math. Soc. Ser. A 41 (1986), 233–236. DOI