**News**

Needless to say, it has been an unusual year. As Covid-19 began its spread throughout the world, The University of Western Australia closed its doors in late March and we all worked from home. Some things were put on hold, but some new innovations arose, such as online Zoom seminars, attracting more visitors than we would usually receive in our weekly seminar series. In this newsletter, which has been 1 year in the waiting, we go over some of the events that we have been involved in since August 2019.

Jesse Lansdown (a PhD student of John Bamberg, Gordon Royle, and Alice Niemeyer) has recently submitted his PhD thesis.

Mark Ioppolo has completed his PhD (supervised by John Bamberg, Alice Devillers, and Cheryl Praeger). Congratulations Mark!

Jack Saunders will be starting a research associate position in the CMSC (primarily working with Michael) in November (2020).

Jesse Lansdown has just begun a research associate position in the CMSC (primarily working with John, Michael, and Gordon).

Carlisle King left the CMSC (December 2019).

Alex Bors has left to do the final year of his Austrian Science Fund Fellowship in Linz.

Anurag Bishnoi arrived to begin his DECRA in November (2019). He will be soon taking up a continuing position at TU Delft (Netherlands).

The Groups and Combinatorics Seminar is currently being held via Zoom (with international audience and speakers).

Cheryl was a Kirk Distinguished Visiting Fellow, taking part in the Isaac Newton Institute semester program:

*Groups, representations and applications: new perspectives*, She gave the Kirk Lecture : The Mathematics of Shuffling.Cheryl: On International Women in Mathematics day a preview was released: 2020 – Preview of Australian Women in Mathematics Exhibition (webpage)

Cheryl: YouTube Video for International Women in Mathematics Day May 12, created for ACEMS

Cheryl features in the 2020-Video on Girls in STEM Toolkit website (see also https://www.thegist.edu.au)

Cheryl was a Member or the Nominating Committee for International Commission for Mathematical Instruction. Because of the coronavirus pandemic, the International Congress of Mathematics Education in Shanghai was postponed and an electronic ICMI General Assembly was held on July 13 2020 at which the next executive was elected.

Michael was at The Isaac Newton Institute for the Groups, representations and applications: new perspectives program for January and and then again in March before the Institute closed down due to coronavirus.

Michael gave a talk entitled “Simple groups and graph symmetry” as part of the associated workshop "Interactions between group theory, number theory, combinatorics and geometry”. Michael also gave the talk “Automorphism orbits of groups and the Monster” at the programme.

## Grants

*"Exceptionally symmetric combinatorial designs",*Alice Devillers and Cheryl Praeger, Australian Research Council Discovery Project.*"The synchronisation hierarchy of permutation groups",*John Bamberg, Michael Giudici, and Gordon Royle, Australian Research Council Discovery Project.

**CMSC Annual Retreat**

The annual CMSC research retreat took place in the week of 3-7 February this year. Once again, we stayed in the Moondyne Country Convention Centre in the marvellous Avon Valley and enjoyed the exceptional hospitality of our hosts Christine and Peter.

We had two external visitors this year: Mariagrazia Bianchi from the University of Milan, and our former colleague Alex Bors (University of Linz).

Altogether, this year's retreat had 10 participants, who worked on 6 problems. We look forward to sharing our insights in the form of publications, and to returning to this very productive research event next year as well.

When UWA re-opened, we had a second edition of our retreat from June 30 & July 1, but this time, at UWA. The photo above is from this year's retreat at Moondyne.

**CMSC ECR Paper Prize**

The 2020 paper prize was awarded to **Yian Xu** for her paper *Constructing 2-arc-transitive covers of hypercubes*. Congratulations (again) Yian!

**Visitors**

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

Alexander Bors visited in early February (2020).

Mariagrazia Bianchi visited in early February (2020).

Luise-Charlotte Kappe visited in early March (2020).

**Conferences**

Stephen Glasby attended Symmetry in Newcastle on 17 July, 7 August, 2020,

Michael Giudici, Stephen Glasby, and Cheryl Praeger will soon be attending the Ural Workshop on Group Theory and Combinatorics, August 24–30, 2020 (virtual).

Alice Devillers will be speaking (remotely) at "A mathematical Medley" in honour of Marston Conder's recent ONZM, 15-16 September 2020, in Auckland.

John Bamberg gave a virtual CMSA seminar. YouTube video.

John Bamberg spoke in August 2019 at Symmetry in Newcastle.

Cheryl Praeger's list of conferences:

2019, December 9-13, ACCMCC conference UNSW – plenary speaker, https://conferences.maths.unsw.edu.au/event/3/

2019, December 16-17, Finite Geometry: a workshop in honour of Tim Penttila, University of Adelaide – featured speaker https://penttilafest.wordpress.com/

2020, January 27-31. Isaac Newton Institute Cambridge. “Computational algorithmic groups workshop”; invited lecture: video at https://www.newton.ac.uk/seminar/20200131134514351

2020, February 6. London Algebra Colloquium, City University

2020, February 20. Birmingham University Algebra Seminar

2020, February 26. Bristol University Algebra and Geometry Seminar

2020, March 6. University of Durham, Faculty Colloquium

2020, March 16-18. Isaac Newton Institute Cambridge. “Interactions of group theory and other areas workshop”; Kirk Lecture.

2020, May 7. Opening “GOTHIC lecture” for the “Ischia Online Group Theory Conference”. [Conference had been cancelled due to corona virus, replaced by the online conference] video available at: https://drive.google.com/file/d/1ZJxLdfnMihho1TElulsjlKVe540t1yE2/view

2020 May 22, Faculty Colloquium RWTH Aachen by ZOOM

2020 June Plus Magazine podcast, Mathematics of Shuffling (Interview with Rachel Tomas)

2020 June 23, “Colloquium Patavina” (Padova, Italy, by ZOOM) (https://www.math.unipd.it/~conti/colloquia/colloquia.html)

2020 June 30, North East Combinatorics Network (US) Virtual Combinatorics Colloquium

2020 August 24-30, Ural Workshop on Group Theory and Combinatorics (virtual)

**Papers**

### Published papers

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. doi

John Bamberg and Klaus Metsch, On intriguing sets of the Penttila-Williford association scheme, Linear Algebra and its Applications 582 (2019), no. 1 (December), 327-345. doi

John Bamberg, Saul D. Freedman and Luke Morgan. On

*p*-groups with automorphism groups related to the Chevalley group*G2(p)*, Journal of the Australian Mathematical Society 108 (2020), no. 3, pp. 321- 331. doiDaniela Bubboloni, Cheryl E Praeger and Pablo Spiga, Linear bounds for the normal covering number of the symmetric and alternating groups. Monatsh. Math. 191, (2020) 229-247. doi

Timothy C. Burness and Michael Giudici. On the Saxl graph of a permutation group. Math. Proc. Cambridge Philos. Soc., 268 (2020) 219-248. doi

Alexander Y. Chua, Michael Giudici, and Luke Morgan. Coprime subdegrees of twisted wreath permutation groups. Proc. Edin. Math. Soc., 62 (2019) 1137-1162. doi

Alice Devillers and Stephen Glasby, Roots of unity and unreasonable differentiation, Archiv der Mathematik 113(4) (2019), 367--371. doi

Alice Devillers, Joanna Fawcett, Cheryl E. Prager, Jin-Xin Zhou, On k-connected-homogeneous graphs, Journal of Combinatorial Theory, Series A 173 (2020) doi

Neil I. Gillespie and Daniel R. Hawtin and Cheryl E Praeger, 2-Neighbour-Transitive Codes with Small Blocks of Imprimitivity. Electronic J. Combin. 27, (2020) P1.42, Pub. 29-01-2020 doi

Michael Giudici, Cai Heng Li, and Yian Xu. Constructing 2-arc-transitive covers of hypercubes. Graphs and Combinatorics, 35 (2019) 973-987. doi

S. P. Glasby, Classifying uniformly generated groups, Commun. Algebra 48 (2020), 101-104. doi

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) (2020), 1827-1852. doi

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

Daniel R. Hawtin and Cheryl E Praeger, Minimal binary 2-neighbour-transitive codes. J. Combin. Theory Series A 171, (2020), 105-173. doi

Jesse Lansdown and Alice Niemeyer, A family of hemisystems on the parabolic quadrics, Journal of Combinatorial Theory, Series A 175 (2020) doi

Martin W. Liebeck, Cheryl E Praeger, and Jan Saxl. The classification of 3/2-transitive permutation groups and 1/2-transitive linear groups. Proc. Amer. Math. Soc. 147 (2019), 5023-5037. doi

There were also some other publications involving Cheryl Praeger:

World Women in Mathematics 2018 - Proceedings of the First World Meeting for Women in Mathematics (WM)², published December 2019 with the eBook to follow on January 18, 2020.

Non-mathematical: Interview published in the IMU Committee for Women in Mathematics Newsletter May 2020, pp. 2-9.

2018 MATRIX ANNALS, Editors: Editor-in-chief: Wood, David R.de Gier, Jan, Praeger, Cheryl E., Tao, Terence (Eds.), Springer 2020

### Accepted papers

Seyed Hassan Alavi and Ashraf Daneshkah and Cheryl E Praeger, Symmetries of biplanes, Designs, Codes and Crypt. arXiv

Carmen Amarra and Luke Morgan and Cheryl E Praeger, Generalised shuffle groups, Israel J Math. arXiv

John Bamberg, Cai-Heng Li, and Eric Swartz, A classification of finite locally 2-transitive generalized quadrangles, Transactions of the American Mathematical Society. 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 GeneticsMariagrazia Bianchi and S. P. Glasby and Cheryl E Praeger, Conjugacy class sizes in arithmetic progression. J. Group Theory. doi

Alice Devillers, Hogxue Liang, Cheryl E. Prager, Binzhou Xia, On flag-transitive 2-(v,k,2) designs, J. Combin. Theory Ser A., arXiv

Alice Devillers, Joanna Fawcett, Cheryl E Praeger and Jin-Xin Zhou, On k-connected-homogeneous graphs. J. Combin. Theory Ser. A Accepted 5 February, 2020. arXiv

Michael Giudici and Gabriel Verret. Arc-transitive graphs of valency twice a prime admit a semiregular automorphism. Ars Math. Comtemp., doi

### Submitted papers

**R. A. Bailey, Peter Cameron, Cheryl E. Praeger and Csaba Schneider, The geometry of diagonal groups. Submitted 1 August 2020.****arXiv****R. A. Bailey, Peter J. Cameron, Michael Giudici, and Gordon F. Royle. Groups generated by derangements.****Alexander Bors and Michael Giudici. Finite transitive permutation groups with only small normaliser orbits.****John Bamberg, Alice Devillers, Joanna Fawcett, Cheryl Praeger, Partial linear spaces with a rank 3 affine primitive group of automorphisms, J. London Math. Soc.****arXiv****Alexander Bors, and Michael Giudici and Cheryl E. Praeger, Automorphism orbits and element orders in finite groups: almost-solubility and the Monster,****arXiv****. "Documentation for the GAP code file OrbOrd.txt" associated with this paper is available at****arXiv****Alice Devillers and Cheryl E. Praeger, On flag-transitive imprimitive 2-designs,****arXiv****Michael Giudici and Carlisle S.H. King, Edge-primitive 3-arc-transitive graphs.****Michael Giudici, Luke Morgan, and Yian Xu, The NNN-property of cyclic groups.****Stephen Glasby, Cheryl E Praeger and William R. Unger, Most permutations power to a cycle of small prime length,****arXiv****Daniel Horsley and Moharram Iradmusa and Cheryl E Praeger, Generating infinite digraphs by derangements.****arXiv**