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

Dave Witte Morris, University of Lethbridge,Lethbridge, Canada
2020 Symmetry, Integrability and Geometry: Methods and Applications  
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
more » ... ubgroups. We generalize (a slightly weakened version of) this by showing that every S-arithmetic subgroup of an isotropic, almost-simple Q-group is quasi-isometrically boundedly generated by standard Q-rank-1 subgroups.
doi:10.3842/sigma.2020.012 fatcat:hxd37tdbqraqjbobfuibg5z4lq