Growth in solvable subgroups of \(\mathrm{GL}_r(\mathbb Z/p\mathbb Z)\).
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Publication:464139
DOI10.1007/s00208-014-1008-8zbMath1308.20043arXiv1008.5264OpenAlexW1235945937MaRDI QIDQ464139
Nick Gill, Harald Andrés Helfgott
Publication date: 17 October 2014
Published in: Mathematische Annalen (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1008.5264
Linear algebraic groups over finite fields (20G40) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Generators, relations, and presentations of groups (20F05) Asymptotic properties of groups (20F69) Arithmetic combinatorics; higher degree uniformity (11B30)
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Cites Work
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- On the sum of two sets in a group
- Expansion in \(\mathrm{SL}_d(\mathcal O_K/I)\), \(I\) square-free.
- Approximate subgroups of linear groups.
- Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order.
- A sum-product estimate in finite fields, and applications
- The structure of approximate groups.
- Product set estimates for non-commutative groups
- Growth and generation in \(\text{SL}_2(\mathbb{Z}/p\mathbb{Z})\).
- Uniform expansion bounds for Cayley graphs of \(\text{SL}_2(\mathbb F_p)\).
- Growth in \(\mathrm{SL}_3(\mathbb Z/p\mathbb Z)\).
- On the spectral gap for finitely-generated subgroups of \(\text{SU}(2)\)
- Rationality properties of linear algebraic groups. II
- Éléments unipotents et sous-groupes paraboliques de groupes réductifs. I
- Approximate groups and doubling metrics
- Freiman's theorem in an arbitrary nilpotent group
- Growth in SL2 over finite fields
- Approximate groups. I The torsion-free nilpotent case
- APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE
- Growth of Small Generating Sets in SLn(Z/pZ)
- Stable group theory and approximate subgroups
- Growth in finite simple groups of Lie type
- Approximate multiplicative groups in nilpotent Lie groups
- Freiman's theorem for solvable groups
- PRODUCT THEOREMS IN SL2 AND SL3
- Linear algebraic groups.
- Abelian unipotent subgroups of reductive groups
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