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Characters of Finite Groups. Part 2

Ya. G. Berkovich University of Haifa, Haifa, Israel
E. M. Zhmud′ Kharkov University, Kharkov, Ukraine
Available Formats:
Hardcover ISBN: 978-0-8218-0532-9
Product Code: MMONO/181
List Price: $129.00 MAA Member Price:$116.10
AMS Member Price: $103.20 Electronic ISBN: 978-1-4704-4595-9 Product Code: MMONO/181.E List Price:$129.00
MAA Member Price: $116.10 AMS Member Price:$103.20
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List Price: $193.50 MAA Member Price:$174.15
AMS Member Price: $154.80 Click above image for expanded view Characters of Finite Groups. Part 2 Ya. G. Berkovich University of Haifa, Haifa, Israel E. M. Zhmud′ Kharkov University, Kharkov, Ukraine Available Formats:  Hardcover ISBN: 978-0-8218-0532-9 Product Code: MMONO/181  List Price:$129.00 MAA Member Price: $116.10 AMS Member Price:$103.20
 Electronic ISBN: 978-1-4704-4595-9 Product Code: MMONO/181.E
 List Price: $129.00 MAA Member Price:$116.10 AMS Member Price: $103.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$193.50 MAA Member Price: $174.15 AMS Member Price:$154.80
• Book Details

Translations of Mathematical Monographs
Volume: 1811999; 332 pp
MSC: Primary 20;

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.

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

• Chapters
• 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
• 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
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Volume: 1811999; 332 pp
MSC: Primary 20;

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.

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

• Chapters
• 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
• 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
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