**News**

Cheryl Praeger was awarded the Companion of the Order of Australia. For more details, see the

__ABC News announcement____.__Cheryl Praeger was re-appointed to the MATRIX Advisory Board for the period 2020-2022.

Cheryl Praeger was re-appointed to the Advisory Board of SMRI (University of Sydney Mathematics Research Institute) for the period 2020-2022.

In September the Joseph Banks Secondary College invited Cheryl Praeger as Guest of Honour at their Father and Daughter maths evening, at which their new maths enrichment program, the Cheryl Praeger Mathematics Academy for Girls was launched. A three minute compilation video of the evening

__is here____.____The Latest from Science: Episode 028 Solving Tomorrow’s Problems Today__. From the Australian Academy of Science features Cheryl Praeger and Adam Spencer.Jack Saunders started as a Research Associate on the 11th of January. He is employed on the Discovery project held by Michael Giudici and Luke Morgan.

Lei Chen officially enrolled as a PhD student in October 2020. He is supervised by Michael Giudici and Cheryl Praeger. Lei was due to arrive in February 2020 but was unable to enter the country. We hope that he will be able to come to Perth soon.

John Bamberg, Michael Giudici and Gordon Royle were awarded the 2020 Gavin Brown prize by the Australian Mathematical Society. The prize is awarded for an outstanding and innovative piece of research in the mathematical sciences published by members of the Australian Mathematical Society, in the last 10 years. The prize was awarded for their paper Every flock generalized quadrangle has a hemisystem, published in the Bulletin of the London Mathematical Society.

**Visitors**

For an up to date list of visitors, see here.

Alice Niemeyer (Nov 2020 - Feb 2021) visiting Cheryl Praeger and Stephen Glasby.

Melissa Lee (August 2020-March 2021) .

Tomasz Popiel (August 2020-March 2021).

**Conferences**

Cheryl Praeger gave the

__second talk__in the Visitor Program Lecture Series of the at the IWM (Indian Women and Mathematics), September 27,Cheryl Praeger gave the last seminar of 2020 on December 15, in the Algebraic Graph Theory Seminar, U Waterloo, Canada,

__https://www.youtube.com/playlist?list=PL_x-9BL_zf4EM4THqG6ZIvMbYqXdmz3QY__Alice Devillers talked about “Combinatorial Designs” at the NZ conference A Mathematical Medley, 19-20 November, 2020.

__https://jschillewaert.wixsite.com/mathmedley__Alice Devillers, Stephen Glasby and Michael Giudici attended (remotely) the AustMS annual conference, 8-11 December, 2020.

Alice Devillers talked about “Some recent results on flag-transitive and block-transitive 2-designs” at the CMSA Day on December 15th, 2020.

__http://combinatorics-australasia.org/CMSA-Day.htm__Michael Giudici gave a seminar `Bases for permutation groups and the Saxl graph’ at The University of Primorska (online) on the 7th of December.

Michael Giudici gave a seminar `The synchronisation hierarchy for permutation groups’ in the

__Symmetry in Newcastle__seminar series on the 18th of September.Michael Giudici gave a contributed talk `Groups generated by derangements’ at the Ural workshop on group theory and combinatorics, (online) 24th-30th of August.

Michael Giudici will be an invited speaker at 11th international conference on Iranian Algebraic combinatorics and graph theory to be held March 4-5, 2021 in Urmia University (online).

Michael Giudici will be an invited speaker at the Ischia Group Theory 2020/2021 24 hours Zoom Conference on 25th of March.

Stephen Glasby will be an invited speaker at the Ischia Group Theory Conference 2020/2021 24 hour Zoom conference on 25 March.

Stephen Glasby attended the 2020 Ural Workshop on Group Theory and Combinatorics, Yekaterinburg-Online, Russia, August 24–30, 2020

**Papers**

### Published papers

Seyed Hassan Alavi and Ashraf Daneshkah and Cheryl E. Praeger, Symmetries of biplanes,

*Designs, Codes and Crypt*. Issue 11/2020.__doi__R. A. Bailey and Peter J. Cameron and Michael Giudici and Gordon F. Royle, Groups generated by derangements, Journal of Algebra 572 245--262, 2021.

__doi__John Bamberg and James Evans, No almost simple sporadic group acts primitively on the points of a generalised quadrangle, Discrete Mathematics 344 (2021), no. 4, 112291. doi

John Bamberg, Arun Ram and Jon Xu. The thickness of Schubert cells as incidence structures, Journal of the Australian Mathematical Society 109 (2020), no. 2, pp. 145 -- 156. doi

Sangeeta Bhatia, Attila Egri-Nagy, Andrew Francis, Volker Gebhardt, Cheryl E. Praeger, and Stuart Serdoz, A path-deformation framework for determining weighted genome rearrangement distance.

*Frontiers in Genetics, section Evolutionary and Population Genetics*11:1035, Open Access. (in a special issue on Algebraic and Geometric Phylogenetics).__doi__Cheryl E. Praeger, Jacqui Ramagge and George Willis. A graph-theoretic description of scale-multiplicative semigroups of automorphisms.

*Israel J. Math*. 237, 221-265.__doi__Alice Devillers, Hongxue Liang, Cheryl E. Praeger and Binzhou Xia, On flag-transitive 2-(v,k,2) designs.

*J. Combin. Theory, Series A*177 Article 105309.__doi__Alice Devillers, Joanna Fawcett, Cheryl E. Praeger and Jin-Xin Zhou, On

*k*-connected-homogeneous graphs.*J. Combin. Theory Ser. A***173**, Article 105234,__doi__Wei Jin and Cheryl E. Praeger, Normal quotients of diameter at most two of finite three-geodesic-transitive graphs,

*J. Combin. Theory Ser. A.***178**, Article 105349,__doi__Michael Giudici and Gabriel Verret, Arc-transitive graphs of valency twice a prime admit a semiregular automorphism. Ars Math. Contemp. 18(1) 179-186, 2020.

__doi__

### Accepted papers

Mariagrazia Bianchi, Stephen Glasby and Cheryl E. Praeger, Conjugacy class sizes in arithmetic progression, to appear J. Group Theory.

__arxiv__Alexander Bors, Michael Giudici, and Cheryl E. Praeger, Automorphism orbits and element orders in finite groups: almost-solubility and the Monster,

*Memoirs Amer. Math. Soc.*Accepted 2 November 2020.__arxiv__. In addition: "Documentation for the GAP code file OrbOrd.txt" associated with this paper is available__here__.Daniel Horsley and Moharram Iradmusa and Cheryl E. Praeger, Generating infinite digraphs by derangements.

*Quarterly J. Math*__doi__Luke Morgan, Cheryl E. Praeger and Kyle Rosa, Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree.

*Proc. Edinburgh Math. Soc*. Published Online 5 November, 2020.__doi____arxiv__Nemanja Poznanovic and Cheryl E. Praeger, Four-valent oriented graphs of biquasiprimitive type,

*Algebraic Combin.*Accepted December 22, 2020.__arxiv__Cheryl E. Praeger,

*Codes and designs in Johnson graphs with high symmetry*, to appear in the Proceedings of the British Combinatorics Colloquium, 2021, Cambridge University Press, Accepted November 14, 2020.

### Submitted papers

Carmen Amarra, Alice Devillers, Cheryl E. Praeger, Delandtsheer-Doyen parameters for block-transitive imprimitive 2-designs.

__arxiv__R. A. Bailey, Peter J. Cameron, Michael Kinyon, and Cheryl E. Praeger, Diagonal groups and arcs over groups.

__arxiv__John Bamberg, Anurag Bishnoi, and Thomas Lesgourges. The minimum degree of minimal Ramsey graphs for cliques.

__arxiv__John Bamberg, Giusy Monzillo, and Alessandro Siciliano. Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes.

John Bamberg, Alexander Bors, Alice Devillers, Michael Giudici, Cheryl E. Praeger, and Gordon Royle. Orbits of Sylow subgroups of finite permutation groups,

__arxiv__Alexander Bors and Stephen Glasby, Finite 2-groups with exactly three automorphism orbits,

__arxiv__Dmitry Churikov and Cheryl E. Praeger, Finite totally k-closed groups. Submitted 3 December 2020.

__arxiv__Michael Giudici, Stephen Glasby and Cheryl E. Praeger, Subgroups of Classical Groups that are Transitive on Subspaces.

__arxiv__Behnam Khosravi and Cheryl E. Praeger, Normal edge-transitive Cayley graphs and Frattini-like subgroups. Submitted 8 December, 2020.