Preprints of my (recent) papers are on the arXiv

Publications (and submitted/accepted papers)

  1. S.P. Glasby, Classifying finite groups G with three Aut(G)-orbits, arXiv

  2. S.P. Glasby, Alice Niemeyer and Cheryl E. Praeger, Absolutely irreducible quasisimple linear groups containing elements of order a specified Zsigmondy prime, arXiv

  3. S.P. Glasby and Alexander Bors, Finite 2-groups with exactly three automorphism orbits, arXiv

  4. S.P. Glasby, Alice Niemeyer and Cheryl E. Praeger, Bipartite q-Kneser graphs and two-generated irreducible linear groups, arXiv

  5. 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. arXiv | Magma code

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

  7. 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

  8. 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

  9. 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

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

  11. S.P. Glasby, Alice 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

  12. 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. XX(X) (2022), XX–XX. arXiv

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. 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

  19. 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

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

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

  22. John Bamberg, S.P. Glasby, Luke Morgan and Alice 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

  23. 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

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

  25. S.P. Glasby, Alice 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

  26. 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

  27. 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

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

  29. John Bamberg, S.P. Glasby, Luke Morgan and Alice 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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.

  35. 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

  36. S.P. Glasby, Frank Lübeck, Alice 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

  37. 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

  38. 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

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

  40. 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

  41. 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

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

  43. 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

  44. 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

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

  46. 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.

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

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

  49. 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

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

  51. 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

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

  53. 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)

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

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

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

  57. 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

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

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

  60. 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

  61. 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

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

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

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

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

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

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