Introduction to Approximate Groups

ISBN-13: 9781108456449 / Angielski / Miękka / 2019 / 216 str.

Matthew C. H. Tointon

Opis

Recent years have seen rapid progress in the field of approximate groups, with the emergence of a varied range of applications. Written by a leader in the field, this text for both beginning graduate students and researchers collects, for the first time in book form, the main concepts and techniques into a single, self-contained introduction.

Recenzje

'The book now under reviews offers an excellent introduction … the book is very nicely written, Researchers and fledgling researchers in this area will want to own this book.' Mark Hunacek, The Mathematical Gazette

Spis treści

1. Introduction; 2. Basic concepts; 3. Coset progressions and Bohr sets; 4. Small doubling in abelian groups; 5. Nilpotent groups, commutators and nilprogressions; 6. Nilpotent approximate groups; 7. Arbitrary approximate groups; 8. Residually nilpotent approximate groups; 9. Soluble approximate subgroups GLn(C); 10. Arbitrary approximate subgroups of GLn(C); 11. Applications to growth in groups; References; Index.