Uniform independence in linear groups
By Emmanuel Breuillard, Tsachik Gelander. 2006
63 citations recorded by the source corpus.
We show that for any non-virtually solvable finitely generated group of matrices over any field, there is an integer m such that, given an arbitrary finite generating set for the group, one may find two elements a and b that are both products of at most m generators, such that a and b are free generators of a free subgroup. This uniformity result improves the original statement of the Tits alternative.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/2402d43afca8587d442ba7fb5471402efbfcf16a
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In Algebra and Number Theory
In Geometry and Topology
- P. P. Varj'u
- Emmanuel Breuillard
- Yves Cornulier
- Harald Andrés Helfgott
- Richard Aoun
- Tsachik Gelander
- Adrian Ioana
In Mathematical Physics
Citations in the corpus
- Recent progress on Bernoulli convolutions (2016, background): “See [19] and [14] for related earlier work.”
- A Strong Tits Alternative (2008, background): “Since hAr(V ) = hAr(V ⊥) (see [6]), we also have δ(V ⊥,W⊥) ≤ hAr(V ) + hAr(W ) We will often denote by δv(V ;W ) the term of the sum in (35) correspond- ing to the place v, so that δ(V ;W ) = 1 [K : K0] ∑ v∈VK nv · δv(V ;W ) 6.2.”
- On the joint spectral radius for isometries of non-positively curved spaces and uniform growth (2018, unknown): “7) for symmetric spaces of non-compact type relies on the Bochi inequality for matrices, thus eventually on linear algebra (see the other proof given in [17]).”