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Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups

2020
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Symmetry, Integrability and Geometry: Methods and Applications
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We say that a subset X quasi-isometrically boundedly generates a finitely generated group Γ if each element γ of a finite-index subgroup of Γ can be written as a product γ = x 1 x 2 · · · x r of a bounded number of elements of X, such that the word length of each x i is bounded by a constant times the word length of γ. A. Lubotzky, S. Mozes, and M.S. Raghunathan observed in 1993 that SL(n, Z) is quasi-isometrically boundedly generated by the elements of its natural SL(2, Z) subgroups. We

doi:10.3842/sigma.2020.012
fatcat:hxd37tdbqraqjbobfuibg5z4lq