Characters of Solvable Groups
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-3485-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-3485-4 (ISBN)
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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.
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.
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.
I. Martin Isaacs, University of Wisconsin, Madison, WI.
$/pi$-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
Bibliography
Index
| Erscheinungsdatum | 19.08.2018 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 830 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-3485-7 / 1470434857 |
| ISBN-13 | 978-1-4704-3485-4 / 9781470434854 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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