Free abelian group of rank two
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Definition
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.
Group properties
Property | Meaning | Satisfied? | Explanation |
---|---|---|---|
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 |