APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE
By Emmanuel Breuillard, Ben Joseph Green. 2009
50 citations recorded by the source corpus.
We describe the structure of "K-approximate subgroups'' of solvable subgroups of GL_n(C), showing that they have a large nilpotent piece. By combining this with the main result of our recent paper on approximate subgroups of torsion-free nilpotent groups, we show that such approximate subgroups are efficiently controlled by nilpotent progressions.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a0b6ade0e4fe174b15e54dd0c42ea6de0bfed73c
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In Discrete Mathematics and Combinatorics
- Terence Tao
- Emmanuel Breuillard
- Ben Joseph Green
- Ehud Hrushovski
- E. Szab'o
- László Pyber
- Nikos Frantzikinakis
- William T. Gowers
In Geometry and Topology
- Terence Tao
- Emmanuel Breuillard
- Ben Joseph Green
- László Pyber
- E. Szab'o
- Ehud Hrushovski
- Nikos Frantzikinakis
- Tom Sanders
Citations in the corpus
- The structure of approximate groups (2011, result): “ank and step OK(1) and |P| ≫K |A|. Furthermore, Pcan be taken to be in OK(1)-normal form. We remark that precursor results to this theorem in the case of nilpotent or solvable groups were obtained in [5, 6, 13, 17, 51, 52]. Theorem 2.10 also provides an independent proof of a qualitative version of ”
- Growth in finite simple groups of Lie type of bounded rank (2010, background): “Actually, in that case, using [11] they deduce a stronger conclusion: one can even require Γ to be nilpotent.”
- Stable group theory and approximate subgroups (2009, background): “ell as polycyclic. Now any polycyclic group is linear over C; see chapter 4 of [45] for a stronger result, due to Auslander-Swan. Hence G0 can be viewed as a solvable subgroup of GLn(C); according to [4], every k-approximate subgroup of G0 is covered by a bounded number of cosets of a (n−1)-step nil”