Finite simple groups and their subgroups

Abstract

The material in this article corresponds roughly to the contents of six lectures given at the International Symposium on Group Theory at Peking University in September 1984. In essence the article describes the beginnings of a theory of permutation representations of finite groups based on the classifications of the finite simple groups. Chapter 3 is devoted to an outline of the Classification, with emphasis on recent efforts to improve the proof of the Classification Theorem. Chapters, 1, 2, and 6 discuss finite groups themselves, a notion of geometry due to J. Tits, and a class of group theoretical techniques introduced by B. Fischer. Each of these topics plays a role in the theory of permutation representations under discussion. The heart of the theory is the study of the subgroup structure of the finite simple groups. Certain results on this structure are described in Chapter 4 and 5.

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