Characters of solvable groups

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. Content: $\pi$-theory: $\pi$-separable groups and character theory background$\pi$-special charactersPartial charactersThe nucleus and $B_\pi$-characters$\mathbf{B}_\pi(G)$ and $\mathbf{I}_\pi(G)$Character counts and correspondences: The Okuyama-Wajima argumentFully ramified abelian sectionsFully ramified sections and character correspondencesM-groups: M-groups and monomial charactersSymplectic modules and character theoryBibliographyIndex Explores 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.