Editing Lattice (group) (section)

==In Lie groups==
{{Main|Lattice (discrete subgroup)}}
More generally, a '''lattice''' Γ in a [[Lie group]] ''G'' is a [[discrete subgroup]], such that the [[Quotient group|quotient]] ''G''/Γ is of finite measure, for the measure on it inherited from [[Haar measure]] on ''G'' (left-invariant, or right-invariant—the definition is independent of that choice). That will certainly be the case when ''G''/Γ is [[compact space|compact]], but that sufficient condition is not necessary, as is shown by the case of the [[modular group]] in [[SL2(R)|''SL''<sub>2</sub>('''R''')]], which is a lattice but where the quotient isn't compact (it has ''cusps''). There are general results stating the existence of lattices in Lie groups.

A lattice is said to be '''uniform''' or '''cocompact''' if ''G''/Γ is compact; otherwise the lattice is called '''non-uniform'''.