Free abelian group of rank two
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This group, denoted or , is defined in the following equivalent ways:
- It is the free abelian group of rank two.
- It is the external direct product of two copies of the group of integers.
- It is the abelianization of free group:F2.
|abelian group||any two elements commute||Yes|
|torsion-free group||no nonzero elements of finite order||Yes|
|finitely generated group||has a finite generating set||Yes|