Freiman's theorem in an arbitrary nilpotent group

DOI10.1112/plms/pdu005zbMath1367.11019arXiv1211.3989OpenAlexW2137285381MaRDI QIDQ2921104

Matthew C. H. Tointon

Publication date: 30 September 2014

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.3989

Mathematics Subject Classification ID

Nilpotent groups (20F18) Inverse problems of additive number theory, including sumsets (11P70) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (12)

Non-commutative methods in additive combinatorics and number theory ⋮ Small doubling in ordered nilpotent groups of class 2 ⋮ Approximate subgroups of residually nilpotent groups ⋮ Nilprogressions and groups with moderate growth ⋮ Growth in Some Finite Three-Dimensional Matrix Groups ⋮ Growth in solvable subgroups of \(\mathrm{GL}_r(\mathbb Z/p\mathbb Z)\). ⋮ Growth and expansion in algebraic groups over finite fields ⋮ A finitary structure theorem for vertex-transitive graphs of polynomial growth ⋮ Polylogarithmic bounds in the nilpotent Freiman theorem ⋮ Properness of nilprogressions and the persistence of polynomial growth of given degree ⋮ Polynomials and harmonic functions on discrete groups ⋮ Growth in groups: ideas and perspectives

Cites Work

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• Generalized arithmetical progressions and sumsets
• A polynomial bound in Freiman's theorem.
• The structure of approximate groups.
• On the Bogolyubov-Ruzsa lemma
• Product set estimates for non-commutative groups
• A nilpotent Freiman dimension lemma
• Approximate groups. I The torsion-free nilpotent case
• Freiman's theorem in an arbitrary abelian group

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