Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups
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 = x₁x₂⋯xᵣ of a bounded number of elements of X, such that the word length of each xᵢ is bounded by a constant times the word len...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210598 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups. Dave Witte Morris. SIGMA 16 (2020), 012, 17 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 = x₁x₂⋯xᵣ of a bounded number of elements of X, such that the word length of each xᵢ 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 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.
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| ISSN: | 1815-0659 |