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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210598 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups. Dave Witte Morris. SIGMA 16 (2020), 012, 17 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862732126628085760 |
|---|---|
| author | Morris, Dave Witte |
| author_facet | Morris, Dave Witte |
| citation_txt | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups. Dave Witte Morris. SIGMA 16 (2020), 012, 17 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2025-12-17T12:04:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210598 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:04:18Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Morris, Dave Witte 2025-12-12T10:36:24Z 2020 Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups. Dave Witte Morris. SIGMA 16 (2020), 012, 17 pages 1815-0659 2020 Mathematics Subject Classification: 22E40; 20F65; 11F06 arXiv:1908.02365 https://nasplib.isofts.kiev.ua/handle/123456789/210598 https://doi.org/10.3842/SIGMA.2020.012 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. I thank A. Brown, D. Fisher, and S. Hurtado for suggesting this problem, and for their encouragement as I worked toward a solution. Extra thanks are due to D. Fisher for suggesting the generalization to groups with infinite center that is presented in Section 6. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups Article published earlier |
| spellingShingle | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups Morris, Dave Witte |
| title | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups |
| title_full | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups |
| title_fullStr | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups |
| title_full_unstemmed | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups |
| title_short | Quasi-Isometric Bounded Generation by Q-Rank-One Subgroups |
| title_sort | quasi-isometric bounded generation by q-rank-one subgroups |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210598 |
| work_keys_str_mv | AT morrisdavewitte quasiisometricboundedgenerationbyqrankonesubgroups |