Cohomology Of Finite Groups

The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and several of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications. The second edition of the book contains many more mod 2 cohomology calculations for the sporadic simple groups, which have been obtained by the authors together with their collaborators over the past decade. In addition the chapter on group cohomology and invariant theory (Chapter III) has been revised and expanded. New references arising from recent developments in the field have also been added, and the index has been substantially enlarged.