The Atlas of Finite Groups - Ten Years on

ISBN-13: 9780521575874 / Angielski / Miękka / 1998 / 312 str.

R. T. Curtis; R. A. Wilson; Robert Curtis

Opis

The Atlas of Finite Groups, published in 1985, has proved itself to be an indispensable tool to all researchers in group theory and many related areas. The present book is the proceedings of a conference organized to mark the tenth anniversary of the publication of the Atlas, and contains twenty articles by leading experts in the field, covering many aspects of group theory and its applications. There are surveys on recent developments, expository articles, and research papers, as well as a historical article on the development of the Atlas project since 1970. The book emphasizes recent advances in group theory and applications that have been stimulated by the comprehensive collection of information contained in the Atlas, and covers both theoretical and computational aspects of finite groups, modular representation theory, presentations, and applications to the study of surfaces.

Recenzje

'The book is an important addition to the literature …'. European Mathematical Society

Spis treści

1. Symmetric presentations and orthogonal groups C. M. Campbell, G. Havas, S. A. Linton and E. F. Robertson; 2. A constructive recognition algorithm for the special linear group F. Celler and C. R. Leedham-Green; 3. Relations in M666 J. H. Conway and C. S. Simons; 4. A survey of symmetric generation of sporadic simple groups R. T. Curtis; 5. Harish-Chandra theory, q-Schur algebras, and decomposition matrices for finite classical groups G. Hiss; 6. The Meataxe as a tool in computational group theory D. F. Holt; 7. Branching rules for modular projective representations of the symmetric groups J. F. Humphreys; 8. Characters and surfaces: a survey G. A. Jones; 9. On the characterization of finite groups by characters W. Kimmerle; 10. Finite linear groups of small degree A. S. Kondratiev; 11. Minimal parabolic systems for the symmetric and alternating groups W. Lempken, C. Parker and P. Rowley; 12. Probabilistic methods in the generation of finite simple groups M. W. Liebeck and A. Shalev; 13. Condensing tensor product modules K. Lux and M. Wiegelmann; 14. Intersections of Sylow subgroups in finite groups V. Mazurov and V. I. Zenkov; 15. Anatomy of the monster S. P. Norton; 16. An integral 'Meat-axe' R. A. Parker; 17. Finite rational matrix groups: a survey W. Plesken; 18. Chamber graphs of sporadic group geometries P. Rowley; 19. An Atlas of sporadic group representations R. A. Wilson; 20. Presentations of reductive Fischer groups F. Zara; 21. Historical remarks J. H. Conway, R. T. Curtis and R. A. Wilson.