03586nam a22005895i 4500 978-3-031-50706-9 DE-He213 20251030111815.0 cr nn 008mamaa 240412s2024 sz | s |||| 0|eng d 9783031507069 978-3-031-50706-9 10.1007/978-3-031-50706-9 doi QA1-939 PB bicssc MAT000000 bisacsh PB thema Cossey, James. author. aut http://id.loc.gov/vocabulary/relators/aut 75070 Characters and Blocks of Solvable Groups [electronic resource] : A User’s Guide to Large Orbit Theorems / by James Cossey, Yong Yang. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. IX, 159 p. 1 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthesis Lectures on Mathematics & Statistics, 1938-1751 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. 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. Mathematics. 65523 Algebra. 1501 Algebras, Linear. 71217 Group theory. 70149 Mathematics Data processing. 65715 Mathematics. 65523 Algebra. 1501 Linear Algebra. 71220 Group Theory and Generalizations. 70154 Applications of Mathematics. 65529 Computational Mathematics and Numerical Analysis. 66073 Yang, Yong. author. aut http://id.loc.gov/vocabulary/relators/aut 75071 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031507052 Printed edition: 9783031507076 Printed edition: 9783031507083 Synthesis Lectures on Mathematics & Statistics, 1938-1751 https://doi.org/10.1007/978-3-031-50706-9 ZDB-2-SXSC 59091 59091