Some non-maximal arithmetic groups
Let k be a non-finite Dedekind domain, and σ be the ring of its integers. We shall assume that the ring R = σ/ (2) is finite. Let us denote by Mn (k) (resp. Mn(σ) ) the ring of all n by n matrices with entries in k (resp. in σ), and Gln (k) its group of units.We denote by sln (k) the subgroup of Gln...
- Autores:
-
Allan, Nelo
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 1968
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/42019
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/42019
http://bdigital.unal.edu.co/32116/
- Palabra clave:
- 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Teoría de los números
grupos discontinuos
grupos aritméticos
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Let k be a non-finite Dedekind domain, and σ be the ring of its integers. We shall assume that the ring R = σ/ (2) is finite. Let us denote by Mn (k) (resp. Mn(σ) ) the ring of all n by n matrices with entries in k (resp. in σ), and Gln (k) its group of units.We denote by sln (k) the subgroup of Gln (k) whose elements g have determinant, det g, equal to one. Let H ε Mn (σ) be a symmetric matrix, i.e., H = tH where tH denotes the transpose matrix of H. We let G = SO (H) = { g ε Sln (k) l tgHg = H }, and we let Gσ = G∩Mn (σ). We want to exhibit certain H for which Gσ is not maxinal in G, in the sense that there exist a subgroup Δ contains Gσ properly and [Δ : Gσ] is finite. |
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