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Characters of Solvable Groups

I. Martin Isaacs University of Wisconsin, Madison, WI
Available Formats:
Hardcover ISBN: 978-1-4704-3485-4
Product Code: GSM/189
List Price: $94.00 MAA Member Price:$84.60
AMS Member Price: $75.20 Electronic ISBN: 978-1-4704-4725-0 Product Code: GSM/189.E List Price:$94.00
MAA Member Price: $84.60 AMS Member Price:$75.20
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: $141.00 MAA Member Price:$126.90
AMS Member Price: $112.80 Click above image for expanded view Characters of Solvable Groups I. Martin Isaacs University of Wisconsin, Madison, WI Available Formats:  Hardcover ISBN: 978-1-4704-3485-4 Product Code: GSM/189  List Price:$94.00 MAA Member Price: $84.60 AMS Member Price:$75.20
 Electronic ISBN: 978-1-4704-4725-0 Product Code: GSM/189.E
 List Price: $94.00 MAA Member Price:$84.60 AMS Member Price: $75.20 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:$141.00 MAA Member Price: $126.90 AMS Member Price:$112.80
• Book Details

Graduate Studies in Mathematics
Volume: 1892018; 368 pp
MSC: Primary 20;

This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups.

It is subdivided into three parts: $\pi$-theory, character correspondences, and M-groups. The $\pi$-theory section contains an exposition of D. Gajendragadkar's $\pi$-special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included.

Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.

Readership

Undergraduate and graduate students and researchers interested in solvable groups, character theory, and finite group theory.

• Table of Contents

• $\pi$-theory
• $\pi$-separable groups and character theory background
• $\pi$-special characters
• Partial characters
• The nucleus and $B_\pi$-characters
• $\mathbf {B}_\pi (G)$ and $\mathbf {I}_\pi (G)$
• Character counts and correspondences
• The Okuyama–Wajima argument
• Fully ramified abelian sections
• Fully ramified sections and character correspondences
• M-groups
• M-groups and monomial characters
• Symplectic modules and character theory
• Additional Material

• Reviews

• [This book] is written in a clear and accurate, yet leisurely style. This makes it an excellent basis for self-study, as well as for a lecture course...It is particularly fortunate to have this bulk of material, up until now scattered throughout the literature, available in a single reference, and developed in a uniform manner.

Gerhard Hiss, Mathematical Reviews
• More than a century after its creation, the character theory of finite groups is still a powerful method for studying finite groups. In the book under review, the focus is on the character theory of groups with many normal subgroups, such as solvable groups. The author has collected in book form many results that before were dispersed on the literature. The presentation is systematic and accessible...If your mathematical tastes lie within the realm of finite groups, the book will not disappoint you.

Felipe Zaldivar, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1892018; 368 pp
MSC: Primary 20;

This book, which can be considered as a sequel of the author's famous book Character Theory of Finite Groups, concerns the character theory of finite solvable groups and other groups that have an abundance of normal subgroups.

It is subdivided into three parts: $\pi$-theory, character correspondences, and M-groups. The $\pi$-theory section contains an exposition of D. Gajendragadkar's $\pi$-special characters, and it includes various extensions, generalizations, and applications of his work. The character correspondences section proves the McKay character counting conjecture and the Alperin weight conjecture for solvable groups, and it constructs a canonical McKay bijection for odd-order groups. In addition to a review of some basic material on M-groups, the third section contains an exposition of the use of symplectic modules for studying M-groups. In particular, an accessible presentation of E. C. Dade's deep results on monomial characters of odd prime-power degree is included.

Very little of this material has previously appeared in book form, and much of it is based on the author's research. By reading a clean and accessible presentation written by the leading expert in the field, researchers and graduate students will be inspired to learn and work in this area that has fascinated the author for decades.

Readership

Undergraduate and graduate students and researchers interested in solvable groups, character theory, and finite group theory.

• $\pi$-theory
• $\pi$-separable groups and character theory background
• $\pi$-special characters
• Partial characters
• The nucleus and $B_\pi$-characters
• $\mathbf {B}_\pi (G)$ and $\mathbf {I}_\pi (G)$
• Character counts and correspondences
• The Okuyama–Wajima argument
• Fully ramified abelian sections
• Fully ramified sections and character correspondences
• M-groups
• M-groups and monomial characters
• Symplectic modules and character theory
• [This book] is written in a clear and accurate, yet leisurely style. This makes it an excellent basis for self-study, as well as for a lecture course...It is particularly fortunate to have this bulk of material, up until now scattered throughout the literature, available in a single reference, and developed in a uniform manner.

Gerhard Hiss, Mathematical Reviews
• More than a century after its creation, the character theory of finite groups is still a powerful method for studying finite groups. In the book under review, the focus is on the character theory of groups with many normal subgroups, such as solvable groups. The author has collected in book form many results that before were dispersed on the literature. The presentation is systematic and accessible...If your mathematical tastes lie within the realm of finite groups, the book will not disappoint you.

Felipe Zaldivar, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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