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Characters and Blocks of Solvable Groups: A User’s Guide to Large Orbit Theorems (Synthesis Lectures on Mathematics & Statistics) - Softcover

Cossey, James; Yang, Yong

 
9783031507083: Characters and Blocks of Solvable Groups: A User’s Guide to Large Orbit Theorems (Synthesis Lectures on Mathematics & Statistics)
Softcover
ISBN 10: 3031507088 ISBN 13: 9783031507083
Publisher: Springer, 2025

Synopsis

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.

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About the Author

James P. Cossey, Ph.D., is a Professor in the Department of Mathematics at Akron University, where he began working in 2008. He received his Ph.D. in mathematics from the University of Wisconsin in 2005, under the supervision of Dr. I.M. Isaacs, with a dissertation entitled “Generalizations of the Fong-Swan Theorem”.  He then served as a postdoctoral fellow at the University of Arizona. He has published about twenty papers in the representation theory of solvable groups and symmetric groups, and has spoken at a number of conferences.


Yong Yang, Ph.D., is an Associate Professor in the Department of Mathematics at Texas State University, where he began working in 2013. He has also been the program director of a math REU site at Texas State University since 2019. He received his Ph.D. in mathematics from the University of Florida in 2009, under the supervision of Dr. Alexandre Turull, with a dissertation entitled “Orbits of the actions of finite solvablegroups”. He has published more than ninety papers in group representation theory. 

From the Back Cover

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

"About this title" may belong to another edition of this title.

Publisher
Springer
Publication date
2025
Language
English
ISBN 10 
3031507088
ISBN 13 
9783031507083
Binding
Paperback
Number of pages
168