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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.Read more
- Written by one of the world leaders in the field
- Gives a comprehensive overview of the subject, including descriptions of related results at the end of each chapter
- Brings together for the first time results that were spread throughout the literature
Reviews & endorsements
'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 ReviewsSee more reviews
'… the author has done an excellent job in presenting a road leading from the basics to the present frontiers in representation theory.' Burkhard Külshammer, zbMATH
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- Date Published: April 2018
- format: Hardback
- isbn: 9781108428446
- length: 250 pages
- dimensions: 235 x 156 x 18 mm
- weight: 0.47kg
- contains: 80 exercises
- availability: In stock
Table of Contents
1. The basics
2. Action on characters by automorphisms
3. Galois action on characters
4. Character values and identities
5. Characters over a normal subgroup
6. Extension of characters
7. Degrees of characters
8. The Howlett–Isaacs theorem
9. Global-local counting conjectures
10. A reduction theorem for the McKay conjecture
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