With the classification of finite groups an era of research in that subject ended. In this symposium volume twenty-nine key figures in the classification programme analyse the likely directions research will take in the future.

This work offers a single source of basic facts about the structure of the finite simple groups with emphasis on a detailed description of their local subgroup structures, coverings, and automorphisms. The method is by examination of the specific groups, rather than by the development of an abstract theory of simple groups. While the purpose of the book is to provide the background for the proof of the classification of the finite simple groups - dictating the choice of topics - the subject matter is covered in such depth and detail that the book should be of interest to anyone seeking...

The theory of finite simple groups enjoyed a period of spectacular activity in the 1950s and 1960s. This title gives an introduction to finite groups and the classification of the simple groups.

The classification of finite simple groups is a landmark result of modern mathematics. The original proof is spread over scores of articles by dozens of researchers. This is the fifth in a multi-volume work in which the authors are assembling the proof with explanations and references. The book, along with background from sections of the previous volumes, presents critical aspects of the classification. In four prior volumes (Surveys of Mathematical Monographs, Volumes 40.1, 40.2, 40.3, and 40.4), the authors began the proof of the classification theorem by establishing certain uniqueness and...

Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be...

Never before in the history of mathematics has there been an individual theorem whose proof has required 10,000 journal pages of closely reasoned argument. Who could read such a proof, let alone communicate it to others? But the classification of all finite simple groups is such a theorem-its complete proof, developed over a 30-year period by about 100 group theorists, is the union of some 500 journal articles covering approximately 10,000 printed pages. How then is one who has lived through it all to convey the richness and variety of this monumental achievement? Yet such an attempt must be...

In February 1981, the classification of the finite simple groups (Dl)* was completed, t. * representing one of the most remarkable achievements in the history or mathematics. Involving the combined efforts of several hundred mathematicians from around the world over a period of 30 years, the full proof covered something between 5,000 and 10,000 journal pages, spread over 300 to 500 individual papers. The single result that, more than any other, opened up the field and foreshadowed the vastness of the full classification proof was the celebrated theorem of Walter Feit and John Thompson in...