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- Arithmetic_group abstract "In mathematics, an arithmetic group (arithmetic subgroup) in a linear algebraic group G defined over a number field K is a subgroup Γ of G(K) that is commensurable with G(O), where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them. It can be shown that this condition depends only on G, not on a given matrix representation of G.Examples of arithmetic groups include therefore the groups GLn(Z). The idea of arithmetic group is closely related to that of lattice in a Lie group. Lattices in that sense tend to be arithmetic, except in well-defined circumstances. The exact relationship of the two concepts was established by the work of Margulis on superrigidity. The general theory of arithmetic groups was developed by Armand Borel and Harish-Chandra; the description of their fundamental domains was in classical terms the reduction theory of algebraic forms.".
- Arithmetic_group wikiPageID "630741".
- Arithmetic_group wikiPageRevisionID "575866867".
- Arithmetic_group hasPhotoCollection Arithmetic_group.
- Arithmetic_group id "a/a013320".
- Arithmetic_group title "Arithmetic group".
- Arithmetic_group subject Category:Algebraic_geometry.
- Arithmetic_group subject Category:Algebraic_groups.
- Arithmetic_group subject Category:Properties_of_groups.
- Arithmetic_group type Abstraction100002137.
- Arithmetic_group type AlgebraicGroups.
- Arithmetic_group type Group100031264.
- Arithmetic_group type Possession100032613.
- Arithmetic_group type PropertiesOfGroups.
- Arithmetic_group type Property113244109.
- Arithmetic_group type Relation100031921.
- Arithmetic_group comment "In mathematics, an arithmetic group (arithmetic subgroup) in a linear algebraic group G defined over a number field K is a subgroup Γ of G(K) that is commensurable with G(O), where O is the ring of integers of K. Here two subgroups A and B of a group are commensurable when their intersection has finite index in each of them. It can be shown that this condition depends only on G, not on a given matrix representation of G.Examples of arithmetic groups include therefore the groups GLn(Z).".
- Arithmetic_group label "Arithmetic group".
- Arithmetic_group label "Arithmetische Gruppe".
- Arithmetic_group sameAs Arithmetische_Gruppe.
- Arithmetic_group sameAs m.02yljs.
- Arithmetic_group sameAs Q4791126.
- Arithmetic_group sameAs Q4791126.
- Arithmetic_group sameAs Arithmetic_group.
- Arithmetic_group wasDerivedFrom Arithmetic_group?oldid=575866867.
- Arithmetic_group isPrimaryTopicOf Arithmetic_group.