Groups St Andrews 2017 in Birmingham
London Mathematical Society Lecture Note Series

Every four years leading researchers gather to survey the latest developments in all aspects of group theory. Initially held in St Andrews, these meetings have become the premier forum for group theory across the whole of the UK. Since 1981, the proceedings of 'Groups St Andrews' have provided a regular snapshot of the state-of-the-art in group theory and helped to shape the direction of research in the field. This volume contains papers from the 2017 meeting held in Birmingham. It includes expository articles from the invited speakers, and further surveys contributed by the participants. Topics include: generation of finite simple groups, block theory, fusion systems, algebraic groups, one-relator groups, geometric group theory, and Beauville groups.

Introduction; 1. Finite simple groups and fusion systems Michael Aschbacher; 2. Finite and infinite quotients of discrete and indiscrete groups Pierre-Emmanuel Caprace; 3. Local-global conjectures and blocks of finite simple groups Radha Kessar and Gunter Malle; 4. A survey on some methods of generating finite simple groups Ayoub B. M. Basheer and Jamshid Moori; 5. One-relator groups: an overview Gilbert Baumslag, Benjamin Fine and Gerhard Rosenberger; 6. New progress in products of conjugacy classes in finite groups Antonio Beltrán, María José Felipe and Carmen Melchor; 7. Aspherical relative presentations all over again William A. Bogley, Martin Edjvet and Gerald Williams; 8. Simple groups, generation and probabilistic methods Timothy C. Burness; 9. Irreducible subgroups of simple algebraic groups – a survey Timothy C. Burness and Donna M. Testerman; 10. Practical computation with linear groups over infinite domains A. S. Detinko and D. L. Flannery; 11. Beauville p-groups: a survey Ben Fairbairn; 12. Structural criteria in factorised groups via conjugacy class sizes María José Felipe, Ana Martínez-Pastor and Víctor Manuel Ortiz-Sotomayor; 13. Growth in linear algebraic groups and permutation groups: towards a unified perspective Harald A. Helfgott; 14. L2-Betti numbers and their analogues in positive characteristic Andrei Jaikin-Zapirain; 15. On the pronormality of subgroups of odd index in finite simple groups Anatoly Kondrat'ev, Natalia Maslova and Danila Revin; 16. Vertex stabilizers of graphs with primitive automorphism groups and a strong version of the Sims conjecture Anatoly S. Kondrat'ev and Vladimir I. Trofimov; 17. On the character degrees of a Sylow p-subgroup of a finite Chevalley group G(pf) over a bad prime Tung Le, Kay Magaard and Alessandro Paolini; 18. Patterns on symmetric Riemann surfaces Adnan Melekoğlu and David Singerman; 19. Subgroups of twisted wreath products Péter P. Pálfy; 20. Some remarks on self-dual codes invariant under almost simple permutation groups B. G. Rodrigues and T. M. Mudziiri Shumba; 21. Test elements: from pro-p to discrete groups Ilir Snopce and Slobodan Tanushevski.

C. M. Campbell is Honorary Reader in the School of Mathematics and Statistics at the University of St Andrews, Scotland. He has co-organised ten Groups St Andrews conferences.
M. R. Quick is Senior Lecturer in the School of Mathematics and Statistics at the University of St Andrews, Scotland. He has co-organised four Groups St Andrews conferences, and he is Deputy Convener of the Proceedings of the Edinburgh Mathematical Society.
C. W. Parker is Professor in the School of Mathematics at the University of Birmingham. He is Editor-in-Chief of the Journal of Group Theory.
E. F. Robertson is Professor Emeritus in the School of Mathematics and Statistics at the University of St Andrews, Scotland.
C. M. Roney-Dougal is Professor in the School of Mathematics and Statistics at the University of St Andrews, Scotland. She is an editor of the Proceedings of the Royal Society of Edinburgh, Section A and a frequent guest on BBC Radio 4's In Our Time.