Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 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 of GLn(C)
- 10 Arbitrary Approximate Subgroups of GLn(C)
- 11 Applications to Growth in Groups
- References
- Index
3 - Coset Progressions and Bohr Sets
Published online by Cambridge University Press: 31 October 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- 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 of GLn(C)
- 10 Arbitrary Approximate Subgroups of GLn(C)
- 11 Applications to Growth in Groups
- References
- Index
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Summary
We introduce coset progressions and Bohr sets, and show that the two notions are roughly equivalent up to Freiman homomorphism. To facilitate the proof of this we introduce lattices and convex bodies and their basic properties, and prove Minkowski’s second theorem from the geometry of numbers.
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- Introduction to Approximate Groups , pp. 35 - 53Publisher: Cambridge University PressPrint publication year: 2019
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