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 (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.

• 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