Assertion: generated abelian group | /r/HasProperty | isomorphic
Facets:
value: to a group of the form
type: OTHER
value: to a finite abelian group
type: OTHER
Source sentences:
text: Any finitely generated abelian group A {\displaystyle A} is isomorphic to the direct sum of r {\displaystyle r} copies of Z {\displaystyle \mathbb {Z} } and a finite abelian group, which in turn is decomposable into a direct sum of finitely many cyclic groups of prime power orders.
text: The primary decomposition formulation states that every finitely generated abelian group G is isomorphic to a direct sum of primary cyclic groups and infinite cyclic groups.
text: That is, every finitely generated abelian group is isomorphic to a group of the form