TY  - BOOK
AU  - Cossey,James
AU  - Yang,Yong
ED  - SpringerLink (Online service)
TI  - Characters and Blocks of Solvable Groups: A User’s Guide to Large Orbit Theorems 
T2  - Synthesis Lectures on Mathematics & Statistics,
SN  - 9783031507069
AV  - QA1-939 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Springer
KW  - Mathematics
KW  - Algebra
KW  - Algebras, Linear
KW  - Group theory
KW  - Data processing
KW  - Linear Algebra
KW  - Group Theory and Generalizations
KW  - Applications of Mathematics
KW  - Computational Mathematics and Numerical Analysis
N1  - Introduction -- Background Material -- Solvable Linear Groups and Gluck’s Permutation Lemma -- Gluck’s Conjecture -- The Huppert ρ-σ Conjecture -- Dolfi’s Theorem -- Induction and Restriction of Characters From p-Complements -- Brauer Graphs of Solvable Groups, I -- Brauer Graphs of Solvable Groups, II -- Conjugacy Classes, Codegrees, Zeros, and other Applications
N2  - This book highlights recent developments in the representation theory of finite solvable groups, which seeks to connect group theory to linear algebra in ways that allow for better study of the groups in question. Over the last several decades, a number of results in the representations of solvable groups have been proven using so-called “large orbit” theorems. This book provides an extensive survey of the current state of the large-orbit theorems. The authors outline the proofs of the large orbit theorems to provide an overview of the topic, then demonstrate how these theorems can be used to prove new results about solvable groups. In addition, this book: Discusses recent developments in the representation theory of finite solvable groups Provides an extensive survey of the current state of the large-orbit theorems, providing a broad overview of the topic Includes proofs that demonstrate how these theorems can be applied to prove new results about solvable groups
UR  - https://doi.org/10.1007/978-3-031-50706-9
ER  -