'Groups St Andrews 2005' was held in the University of St Andrews in August 2005 and this second volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by John Meakin (Lincoln, Nebraska) and Ákos Seress (Ohio State). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

Introduction; 1. Groups and semigroups: connections and contrasts John Meakin; 2. Toward the classification of s-arc transitive graphs Ákos Seress; 3. Non-cancellation group computation for some finitely generated nilpotent groups Habtay Ghebrewold; 4. Permutation and quasi-permutation representations of the Chevalley groups Maryam Ghorbany; 5. The shape of solvable groups with odd order S. P. Glasby; 6. Embedding in finitely presented lattice-ordered groups: explicit presentations for constructions A. M. W. Glass, Vincenzo Marra and Daniele Mundici; 7. A note on abelian subgroups of p-groups George Glauberman; 8. On kernel flatness Akbar Golchin; 9. On proofs in finitely presented groups George Havas and Colin Ramsay; 10. Computing with 4-Engel groups George Havas and M. R. Vaughan-Lee; 11. On the size of the commutator subgroup in finite groups Marcel Herzog, Gil Kaplan and Arieh Lev; 12. Groups of infinite matrices Waldemar Holubowski; 13. Triply factorised groups and nearrings Peter Hubert; 14. On the space of cyclic trigonal Riemann surfaces of genus 4 Milagros Izquierdo and Daniel Ying; 15. On simple Kn-groups for n = 5, 6 A. Jafarzadeh and A. Iranmanesh; 16. Products of Sylow subgroups and the solvable radical Gil Kaplan and Dan Levy; 17. On commutators in groups Luise-Charlotte Kappe and Robert Fitzgerald Morse; 18. Inequalities for the Baer invariant of finite groups Saeed Kayvanfar; 19. Automorphisms with centralizers of small rank Evgeny Khukhro and Victor Mazurov; 20. 2-signalizers and normalizers of Sylow 2-subgroups in finite simple groups Anatoly S. Kondratiev and Victor D. Mazurov; 21. On properties of abnormal and pronormal subgroups in some infinite groups Leonid A. Kurdachenko, Javier Otal and Igor Ya. Subbotin; 22. P-localizing group extensions Karl Lorensen; 23. On the n-covers of exceptional groups of Lie type Maria Silvia Lucido; 24. Positively discriminating groups O. Macedonska; 25. Automorphism groups of some chemical graphs G. A. Moghani, A. R. Ashrafi and M. R. Admadi; 26. On c-normal subgroups of some classes of finite groups Z. Mostaghim; 27. Fong characters and their fields of values Lucia Sanus; 28. Arithmetical properties of finite groups W. J. Shi; 29. On prefrattini subgroups of finite groups: a survey X. Soler-Escrivà; 30. Frattini extensions and class field theory Th. Weigel; 31. The nilpotency class of groups with fixed point free automorphisms of prime order Lawrence Wilson.