C. M. Campbell is an Honorary Reader in the School of Mathematics and Statistics at the University of St Andrews. M. R. Quick is a Senior Lecturer in the School of Mathematics and Statistics at the University of St Andrews. E. F. Robertson is Professor Emeritus in the School of Mathematics and Statistics at the University of St Andrews. C. M. Roney-Dougal is a Senior Lecturer in the School of Mathematics and Statistics at the University of St Andrews. G. C. Smith is a Senior Lecturer in the Department of Mathematical Sciences at the University of Bath. G. Traustason is a Reader in the Department of Mathematical Sciences at the University of Bath.

• Introduction C. M. Campbell and E. F. Robertson; 1. Algorithms for matrix groups E. A. O'Brien; 2. Residual properties of 1-relator groups Mark Sapir; 3. Words and groups Dan Segal; 4. The modular isomorphism problem for the groups of order 512 Bettina Eick and Alexander Konovalov; 5. Recent progress in the symmetric generation of groups Ben Fairbairn; 6. Discriminating groups: a comprehensive overview Benjamin Fine, Anthony M. Gaglione, Alexei Myasnikov, Gerhard Rosenberger and Dennis Spellman; 7. Extending the Kegel–Wielandt theorem through π-decomposable groups L. S. Kazarin, A. Martínez-Pastor and M. D. Pérez-Ramos; 8. On the prime graph of a finite group Behrooz Khosravi; 9. Applications of Lie rings with finite cyclic grading E. I. Khukhro; 10. Pronormal subgroups and transitivity of some subgroup properties Leonid A. Kurdachenko, Javier Otal and Igor Ya. Subbotin; 11. On Engel and positive laws O. Macedońska and W. Tomaszewski; 12. Maximal subgroups of odd index in finite groups with simple classical socle N. V. Maslova; 13. Some classic and nearly classic problems on varieties of groups Peter M. Neumann; 14. Generalizations of the Sylow theorem Danila O. Revin and Evgeny P. Vdovin; 15. Engel groups Gunnar Traustason; 16. Lie methods in Engel groups Michael Vaughan-Lee; 17. On the degree of commutativity of p-groups of maximal class A. Vera-López and M. A. García-Sánchez; 18. Class preserving automorphisms of finite p-groups: a survey Manoj K. Yadav; 19. Symmetric colorings of finite groups Yuliya Zelenyuk.

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