# Publications

## Exciting news!

Tim Penttila and I are currently finishing our new book on projective geometry (over the real numbers) that will be published by Cambridge University Press.

Solutions to selected exercises

## Published papers

Some of the following appear on the open preprint server arxiv.org.

- Non-free points for groups generated by a pair of 2 x 2 matrices,

Journal of the London Mathematical Society (2) 62 (2000), 795–801. - A note on torsion groups generated by pairs of 2 × 2 rational parabolic matrices,

Bulletin of the Australian Mathematical Society 61 (2000), 151–152,

with Grant Cairns. - The crystallographic restriction, permutations, and Goldbach’s Conjecture,

American Mathematical Monthly 110 (2003), 202–209,

with Grant Cairns and Devin Kilminster. - Finite permutation groups with a transitive minimal normal subgroup,

Proceedings of the London Mathematical Society (3) 89 (2004), 71–103,

with Cheryl E. Praeger. - Symplectic spreads,

Designs, Codes and Cryptography 32 (2004), 9–14,

with Simeon Ball, Michel Lavrauw, and Tim Penttila - Totally Goldbach numbers and related conjectures,

Australian Mathematical Society. Gazette 31 (2004), 251–255,

with David van Golstein Brouwers and Grant Cairns. - Bounds and quotient actions of innately transitive groups,

Journal of the Australian Mathematical Society 79 (2005), 95–112. - Transitive eggs,

Innovations in Incidence Geometry 4 (2006), 1–12.

with Tim Penttila. - Tight sets and m-ovoids of finite polar spaces,

Journal of Combinatorial Theory Series A 114 (2007), no. 7, 1293–1314.

with Shane Kelly, Maska Law, and Tim Penttila. - Transitive decompositions of graph products: rank 3 product action type,

Journal of Group Theory 11 (2008), no. 2, 185–228.

with Geoffrey Pearce and Cheryl E. Praeger. - A construction of one-dimensional affine flag-transitive linear spaces,

Finite Fields and their Applications 14 (2008), no. 2, 537-548,

with Michael Pauley. - Overgroups of cyclic Sylow subgroups of linear groups,

Communications in Algebra 36 (2008), no. 7, 2503–2543,

with Tim Penttila. - Elation generalised quadrangles for which the number of lines on a point is the successor of a prime,

Journal of the Australian Mathematical Society 85 (2008), no. 3, 289–303,

with Tim Penttila and Csaba Schneider. - A hemisystem of a nonclassical generalised quadrangle,

Designs, Codes and Cryptography 51 (2009), no. 2, 157–165,

with Frank De Clerck and Nicola Durante. - A classification of transitive ovoids, spread, and m-systems of polar spaces,

Forum Mathematicum 21 (2009), no. 2, 181–216,

with Tim Penttila. - Tight sets and m-ovoids of generalised quadrangles,

Combinatorica 29 (2009), no. 1, 1–17,

with Maska Law and Tim Penttila. - Every flock generalised quadrangle has a hemisystem,

Bulletin of the London Mathematical Society 42 (2010), no. 5, pp. 795–810,

with Michael Giudici and Gordon Royle. arxiv - A geometric construction of Mathon’s perp-system from four lines of PG(5, 3),

Journal of Combinatorial Designs 18 (2010), no. 6, pp. 450–461,

with Frank De Clerck. - Point regular groups of automorphisms of generalised quadrangles,

Journal of Combinatorial Theory Series A, 118 (2011), no. 6, pp. 450–461,

with Michael Giudici. - Intriguing sets of partial quadrangles,

Journal of Combinatorial Designs 19 (2011), no. 3, pp. 217–245,

with Frank De Clerck and Nicola Durante. - Generalised quadrangles with a group of automorphisms acting primitive on points and lines,

Journal of Combinatorial Theory Series A 119 (2012), no. 7, pp. 1479 – 1499,

with Michael Giudici, Joy Morris, Gordon Royle and Pablo Spiga. - Weighted intriguing sets of finite generalised quadrangles,

Journal of Algebraic Combinatorics 36 (2012), no. 1, pp. 149 – 173,

with Alice Devillers and Jeroen Schillewaert. - A classification of the strongly regular generalised Johnson graphs,

Annals of Combinatorics 16 (2012), no. 3, pp. 489 – 506,

with Andrew D. Cannon and Cheryl E. Praeger. - Low dimensional models of the finite split Cayley hexagon,

Contemporary Mathematics 579 (2012), pp. 1 – 20,

with Nicola Durante. - Hemisystems of small flock quadrangles,

Designs, Codes and Cryptography 67 (2013), no. 1, pp. 137 – 157,

with Michael Giudici and Gordon Royle. - An alternative way to generalise the pentagon,

Journal of Combinatorial Designs 21 (2013), no. 4, pp. 163 – 179,

with Simeon Ball, Alice Devillers and Klara Stokes. - The classification of almost simple 3/2-transitive groups,

Transactions of the American Mathematical Society 365 (2013), no. 8, pp. 4257 – 4311,

with Michael Giudici, Martin Liebeck, Cheryl Praeger, and Jan Saxl. - Unitals in the Desarguesian projective plane of order 16,

Journal of Statistical Planning and Inference 144 (2014), pp. 110 – 122.

with Anton Betten, Cheryl Praeger and Alfred Wasserman. - Bounds on the diameter of Cayley graphs of the symmetric group,

Journal of Algebraic Combinatorics 40 (2014), no. 1, pp. 1 – 22.

with Nick Gill, Thomas P. Hayes, Harald A. Helfgott, Ákos Seress and Pablo Spiga. - Editorial: Special issue on finite geometries in honor of Frank De Clerck,

Designs, Codes and Cryptography 72 (2014), no. 1, pp. 1 – 5,

with Jan De Beule, Nicola Durante, and Michael Lavrauw. - AS-configurations and skew-translation generalised quadrangles,

Journal of Algebra (special issue in memory of Ákos Seress) 421 (2015), pp. 311 – 330.

with S. P. Glasby and Eric Swartz. - Triple factorisations of the general linear group and their associated geometries,

Linear Algebra and its Applications 469 (2015), pp. 169–203,

with Seyed Hassan Alavi and Cheryl E. Praeger. - Locally triangular graphs and rectagraphs with symmetry,

Journal of Combinatorial Theory Series A 133 (2015), pp. 1 – 28,

with Alice Devillers, Joanna B. Fawcett, and Cheryl E. Praeger. - Completing Segre’s proof of Wedderburn’s little theorem,

Bulletin of the London Mathematical Society 47 (2015), no. 3, pp. 483 – 492.

with Tim Penttila. - An enumeration of certain projective ternary two-weight codes,

Journal of Combinatorial Designs, 24 (2016), no. 1, pp. 21 – 35,

with Michael Martis and Sylvia Morris. - Generalised quadrangles and transitive pseudo-hyperovals,

Journal of Combinatorial Designs, 24 (2016), no. 4, pp. 151 – 164,

with S. P. Glasby, Tomasz Popiel, and Cheryl E. Praeger. - A note on relative hemisystems of Hermitian generalised quadrangles,

Designs, Codes & Cryptography, 81 (2016), no. 1, pp. 131 – 144,

with Melissa Lee and Eric Swartz. - Point-primitive generalised hexagons and octagons,

Journal of Combinatorial Theory Series A, 147 (2017), pp. 186 – 204,

with S. P. Glasby, Tomasz Popiel, Cheryl Praeger, and Csaba Schneider. - New non-existence proofs for ovoids of Hermitian polar spaces and hyperbolic quadrics,

Annals of Combinatorics, 21 (2017), no 1, pp. 25 – 42,

with Jan De Beule and Ferdinand Ihringer. - Point-primitive, line-transitive generalised quadrangles of holomorph type,

Journal of Group Theory 20 (2017), no. 2, pp. 269 – 287.

with Tomasz Popiel and Cheryl Praeger. - A relative
*m*-cover of the Hermitian surface is a relative hemisystem,

Journal of Algebraic Combinatorics 45 (2017), no. 4, pp. 1217 – 1228.

with Melissa Lee. - Synchronization and separation in the Johnson schemes,

Portugaliae Mathematica 74 (2017), no. 3, pp. 213 – 232.

with Mohammed Aljohani and Peter J. Cameron. - A classification of finite antiflag-transitive generalized quadrangles,

Transactions of the American Mathematical Society 370 (2018), no. 3, pp. 1551 – 1601,

with Cai-Heng Li and Eric Swartz. doi - Bruck nets and partial Sherk planes,

Journal of the Australian Mathematical Society 104 (2018), no. 1, pp. 1 – 12.

with Joanna B. Fawcett and Jesse Lansdown. doi - A new infinite family of hemisystems of the Hermitian surface,

Combinatorica 38 (2018), no. 1, pp. 43 – 66.

with Melissa Lee, Koji Momihara, Qing Xiang. doi - On
*m*-ovoids of regular near polygons,

Designs, Codes & Cryptography 86 (2018), no. 5, pp. 997 – 1006.

with Jesse Lansdown and Melissa Lee. doi - On regular induced subgraphs of bipartite cages,

Journal of Combinatorial Theory Series A 158 (2018), pp. 254 – 275.

with Anurag Bishnoi and Gordon Royle. doi - Maximal linear groups induced on the Frattini quotient of a
*p*-group,

Journal of Pure and Applied Algebra 222 (2018), no. 10, pp. 2931 – 2951,

with S. P. Glasby, Luke Morgan, and Alice Niemeyer. - On the circular altitude of a graph,

Australasian Journal of Combinatorics 72 (2018), no. 2, pp. 357 – 368,

with Brian Corr, Alice Devillers, Daniel Hawtin, Irene Pivotto, and Eric Swartz. doi - On abstract ovals with Pascalian secant lines,

Journal of Group Theory 21 (2018), no. 6, 1051 – 1064,

with Tim Harris and Tim Penttila. doi - The covering radii of the 2-transitive unitary, Suzuki, and Ree groups,

Journal of Group Theory 22 (2019), no. 1, 103 – 117,

with Cheryl E. Praeger and Binzhou Xia. doi - Simple groups, product actions, and generalized quadrangles,

Nagoya Mathematical Journal 234 (2019), 87 – 126.

with Tomasz Popiel and Cheryl Praeger. doi - On intriguing sets of the Penttila-Williford association scheme,

Linear Algebra and its Applications 582 (2019), no. 1 (December), 327 – 345.

with Klaus Metsch. doi - Corrigendum to “Maximal linear groups induced on the Frattini quotient of a p-group’’ [J. Pure Appl. Algebra 222 (10) (2018) 2931–2951].

Journal of Pure and Applied Algebra 223 (2019), no. 12, 5428 – 5429.

with S. P. Glasby, Luke Morgan, Alice C. Niemeyer. - Permutations with orders coprime to a given integer,

Electronic Journal of Combinatorics, 27 (2020), #P1.6,

with Stephen Glasby, Scott Harper, Cheryl E. Praeger. doi - On $p$-groups with automorphism groups related to the Chevalley group $G_2(p)$,

Journal of the Australian Mathematical Society 108 (2020), no. 3, pp. 321 – 331. doi

with Saul D. Freedman and Luke Morgan. - The thickness of Schubert cells as incidence structures,

Journal of the Australian Mathematical Society 109 (2020), no. 2, pp. 145 – 156.

with Arun Ram and Jon Xu. doi - No almost simple sporadic group acts primitively on the points of a generalised quadrangle,

Discrete Mathematics 344 (2021), no. 4, 112291.

with James Evans. doi - A classification of finite locally 2-transitive generalized quadrangles,

Transactions of the American Mathematical Society 374 (2021), no. 3, 1535 – 1578.

with Cai-Heng Li and Eric Swartz. doi - Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes,

Linear Algebra and its Applications 624 (2021), pp. 281–317,

with Giusy Monzillo and Alessandro Siciliano. doi - Partial linear spaces with a rank 3 affine primitive group of automorphisms,

Journal of the London Mathematical Society 104 (2021), no. 3, pp. 1011–1084,

with Alice Devillers, Joanna B. Fawcett, Cheryl E. Praeger. doi - Correction to: New non-Existence proofs for ovoids of Hermitian polar spaces and hyperbolic quadrics.

Annals of Combinatorics 25 (2021), pp. 1095–1097,

with Jan De Beule and Ferdinand Ihringer doi - Orbits of Sylow subgroups of finite permutation groups,

Journal of Algebra 607 (2022), Part A, pp. 107–133,

with Alexander Bors, Alice Devillers, Michael Giudici, Cheryl Praeger, and Gordon Royle. doi - Synchronising primitive groups of diagonal type exist,

Bulletin of the London Mathematical Society 54 (2022), pp. 1131–1144,

with Michael Giudici, Jesse Lansdown, Gordon Royle. doi

## To appear

- The minimum degree of minimal Ramsey graphs for cliques,

Bulletin of the London Mathematical Society,

with Anurag Bishnoi and Thomas Lesgourges. doi - Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry,
Algebraic Combinatorics,

with Jesse Lansdown.

## Submitted

- Codes and designs in Johnson graphs from symplectic actions on quadratic forms,

with Alice Devillers, Mark Ioppolo, Cheryl E. Praeger. - Simpler foundations for the hyperbolic plane,

with Tim Penttila. - FinInG: a package for finite incidence geometry,

with Anton Betten, Philippe Cara, Jan De Beule, Max Neunhoeffer, and Michel Lavrauw.

## In preparation

- Rank 3 separating graphs, with Michael Giudici, Jesse Lansdown, and Gordon Royle.
- Euclidean geometry is incidence geometry, with Tim Penttila.
- On m-ovoids of dual twisted triality hexagons
- Triple factorisations of classical groups by maximal parabolic subgroups and their associated geometries, with Seyed Hassan Alavi and Cheryl E. Praeger.
- On the elation group of the dual of the $H(4,q^2)$ generalised quadrangle, with Michel Lavrauw and Tim Penttila.
- On the geometry of Kantor, with Nicola Durante.
- Classical geometry I. Real Euclidean and Inversive Geometry, with Tim Penttila [book]
- Classical geometry II. Real Affine Geometry, with Tim Penttila [book]
- Classical geometry IV. Foundations of Euclidean geometry. with tim Penttila [book]
- Incidence geometry I. Affine and projective geometry over a field. (with Tim Penttila [book]
- Incidence geometry II. Foundations of affine and projective geometry. (with Tim Penttila) [book]
- Incidence geometry III. Finite geometries. (with Tim Penttila) [book]