The McKay conjecture is the origin of the counting conjectures in the representation theory of finite groups. This book gives a comprehensive introduction to these conjectures, while assuming minimal background knowledge. Character theory is explored in detail along the way, from the very basics to the state of the art. This includes not only older theorems, but some brand new ones too. New, elegant proofs bring the reader up to date on progress in the field, leading to the final proof that if all finite simple groups satisfy the inductive McKay condition, then the McKay conjecture is true. Open questions are presented throughout the book, and each chapter ends with a list of problems, with varying degrees of difficulty.

Presents contemporary character theory of finite groups from the basics to the state of the art, with new, refined proofs.

About the Author
Gabriel Navarro is Professor in the Department of Mathematics at the University of Valencia. He has published over 160 papers, and the widely-cited volume Characters and Blocks of Finite Groups (Cambridge, 1998). He is a leading researcher in character theory and the McKay conjecture.

Reviews
'Navarro continues his informative preface with an exhaustive overview of the work done on this conjecture, and he includes a number of fascinating insights and elaborations.' Michael Berg, MAA Reviews
'... the author has done an excellent job in presenting a road leading from the basics to the present frontiers in representation theory.' Burkhard Kulshammer, zbMATH



Book Information
ISBN 9781108428446
Author Gabriel Navarro
Format Hardback
Page Count 250
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 470g
Dimensions(mm) 235mm * 156mm * 18mm