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arithmetic group
In mathematics, an arithmetic group is a subgroup of a linear algebraic group with simple algebraic properties.
==Formal definition==
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''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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