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Representation Theory of Finite Groups: An Introductory Approach (Universitext)

<p><i>Representation Theory of Finite Groups</i> presents group representation theory at a level accessible to advanced undergraduate students and beginning graduate students. The required background is maintained to the level of linear algebra, group theory, and very basic ring theory and avoids prerequisites in analysis and topology by dealing exclusively with finite groups. Module theory and Wedderburn theory, as well as tensor products, are deliberately omitted. Instead, an approach based on discrete Fourier Analysis is taken, thereby demanding less background from the reader.</p><p></p><p>The main topics covered in this text include character theory, the group algebra and Fourier analysis, Burnside's <i>pq</i>-theorem and the dimension theorem, permutation representations, induced representations and Mackey's theorem, and the representation theory of the symmetric group. For those students who have an elementary knowledge of probability and statistics, a chapter on random walks on

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