The aim of this text is to present some of the key results in
the representation theory of finite groups. In order to keep the
account reasonably elementary, so that it can be used for
graduate-level courses, Professor Alperin has concentrated on local
representation theory, emphasising module theory throughout. In
this way many deep results can be obtained rather quickly. After
two introductory chapters, the basic results of Green are proved,
which in turn lead in due course to Brauer''s First Main Theorem. A
proof of the module form of Brauer''s Second Main Theorem is then
presented, followed by a discussion of Feit''s work connecting maps
and the Green correspondence. The work concludes with a treatment,
new in part, of the Brauer-Dade theory. As a text, this book
contains ample material for a one semester course. Exercises are
provided at the end of most sections; the results of some are used
later in the text. Representation theory is applied in number
theory, combinatorics and in many areas of algebra. This book will
serve as an excellent introduction to those interested in the
subject itself or its applications.
目錄:
Preface
Part I. Semi-Simple Modules
Part II. Projective Modules
Part III. Modules and Subgroups
Part IV. Blocks
Part V. Cyclic Blocks