Characters of Solvable Groups (Graduate Studies in Mathematics) by I. Martin Isaacs (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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[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 About the Author I. Martin Isaacs, University of Wisconsin, Madison, WI.

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