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Representations and characters of groups. (English) Zbl 0792.20006
Cambridge Mathematical Textbooks. Cambridge: Cambridge University Press,. x, 419 p. (1993).
This introductory book to the representation theory of finite groups consists of thirty chapters. Two thirds of the book can be regarded as a standard introduction whose subjects can also be found in several books that appeared over the last twenty years or so (with emphasis on the last ten years). The last third of the book gives some original examples and applications. To mention a few: character calculations of groups of order at most sixteen, of order \(pq\) (\(p\) and \(q\) primes), theory of groups of order \(p^ aq^ b\), character table of the group \(PSL(2,7)\), applications of representation theory to molecular vibrations.
Each chapter has at the end a compendium of the results derived in that chapter. There are also exercises with hints to their solutions.
To summarize, a pretty readable text for students and professionals; the originality of the text is mostly to find in the last third part of the book. The book should be compared to other introductory texts; the reader can best judge about the hows and whys.

20C15 Ordinary representations and characters
20-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to group theory