This two-volume book contains papers from the international conference 'Groups St Andrews 1997 in Bath'.

1. Galois groups through invariant relations J. A. Hulpke; 2. Construction of Co3. An example of the use of an integrated system for computational group theory J. A. Hulpke and S. A. Linton; 3. Embedding some recursively presented groups D. L. Johnson; 4. The Dedekind-Frobenius group determinant: new life in an old problem K. W. Johnson; 5. Group characters and pi-sharpness K. W. Johnson and E. Poimenidou; 6. Permutation group algorithms via black box recognition algorithms W. M. Kantor and A. Seress; 7. Nonabelian tensor products of groups: the commutator connection L.-C. Kappe; 8. Simple subalgebras of generalized Witt algebras of characteristic zero N. Kawamoto; 9. Applications of the Baker-Hausdorff formula in the theory of finite p-groups E. I. Khukhro; 10. Generalizations of the restricted Burnside problem for groups with automorphisms E. I. Khukhro; 11. The Sigmam-conjecture for a class of metabelian groups D. H. Kochloukova; 12. Rings with periodic groups of units II J. Krempa; 13. Some free-by-cyclic groups I. J. Leary, G. A. Niblo and D. T. Wise; 14. The residually weakly primitive geometries of the Suzuki simple group Sz(8) D. Leemans; 15. Semigroup identities and Engel groups P. Longobardi and M. Maj; 16. Groups whose elements have given orders V. D. Mazurov and W. J. Shi; 17. The Burnside groups and small cancellation theory J. P. McCammond; 18. Solvable Engel groups with nilpotent normal closures R. F. Morse; 19. Nilpotent injectors in finite groups A. Neumann; 20. Some groups with right Engel elements W. Nickel; 21. The growth of finite subgroups in p-groups A. Yu. Ol'shanskii; 22. Symplectic amalgams and extremal subgroups C. W. Parker and P. Rowley; 23. Primitive prime divisor elements in finite classical groups C. E. Praeger; 24. On the classification of generalized Hamiltonian groups D. M. Reboli; 25. Permutability properties of subgroups D. J. S. Robinson; 26. When Schreier transversals grow wild A. Rosemann; 27. Probabilistic group theory A. Shalev; 28. Combinatorial methods: from groups to polynomial algebras V. Shpilrain; 29. Formal languages and the word problem for groups I. A. Stewart and R. M. Thomas; 30. Periodic cohomology and free and proper actions on Rn x Sm O. Talelli; 31. On modules over group rings of soluble groups of finite rank A. V. Tushev; 32. On some series of normal subgroups of the Gupta-Sidki 3-group A. C. Vieira.