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Characters of Finite Groups. Part 2
Ya. G. Berkovich, University of Haifa, Israel, and E. M. Zhmud', Kharkov University, Ukraine
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Translations of Mathematical Monographs
1999; 332 pp; hardcover
Volume: 181
ISBN-10: 0-8218-0532-0
ISBN-13: 978-0-8218-0532-9
List Price: US$129
Member Price: US$103.20
Order Code: MMONO/181
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This book places character theory and its applications to finite groups within the reach of people with a comparatively modest mathematical background. The work concentrates mostly on applications of character theory to finite groups. The main themes are degrees and kernels of irreducible characters, the class number and the number of nonlinear irreducible characters, values of irreducible characters, characterizations and generalizations of Frobenius groups, and generalizations of monomial groups. The presentation is detailed, and many proofs of known results are new.

Readership

Graduate students and research mathematicians working in finite group theory and applications.

Reviews

"The reviewer regards the book as a "must", certainly due to the techniques and results offered, it is up to date, and it is ... a very welcome and illuminating contribution in presenting to the mathematical community the beauty of the theory of characters of finite groups."

-- Zentralblatt MATH

Table of Contents

  • Degrees and kernels of irreducible characters
  • Involutions
  • Connectedness and Zassenhaus groups
  • The Nagao theorem
  • Linear groups
  • Permutation characters
  • Characters of SL\((2,p^n)\)
  • Zeros of characters
  • The Schur index
  • On degrees of irreducible components of induced characters
  • Groups in which only two nonlinear irreducible characters have equal degrees
  • Groups with small sums of degrees of some characters
  • On sums of degrees of irreducible characters
  • Groups whose nonlinear irreducible characters take three distinct values
  • Nonsolvable groups with many involutions
  • On kernels of nonlinear irreducible characters
  • On monolithic characters
  • The class number
  • Problems
  • Notes on the bibliography
  • Bibliography
  • Author index
  • Subject index
  • List of corrections to part 1
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