Assertion: free abelian group | /r/HasProperty | isomorphic
Facets:
value: to the group
type: OTHER
Source sentences:
text: This group is unique in the sense that every two free abelian groups with the same basis are isomorphic.
text: The rank of a free abelian group is the cardinality of a basis; every two bases for the same group give the same rank, and every two free abelian groups with the same rank are isomorphic.
text: Every torsion-free Abelian group of rank 1 is isomorphic to some subgroup of the additive group of rational numbers.
text: The free abelian group of rank is isomorphic to a direct sum of copies of the group of integers.
text: In particular, the free abelian group of rank for a natural number is isomorphic to the group , which is a direct product of copies of the group of integers.