Assertion: abelian group | /r/HasProperty | isomorphic
Facets:
value: to the cokernel of linear map
type: OTHER
value: to either z
type: OTHER
value: for another example
type: OTHER
Source sentences:
text: The same can be said for any abelian group of order 15, leading to the remarkable conclusion that all abelian groups of order 15 are isomorphic.
text: For another example, every abelian group of order 8 is isomorphic to either Z 8 {\displaystyle \mathbb {Z} _{8}} (the integers 0 to 7 under addition modulo 8), Z 4 ⊕ Z 2 {
text: Then, the abelian group is isomorphic to the cokernel of linear map defined by M. Conversely every integer matrix defines a finitely generated abelian group.
text: Abelian groups are isomorphic if and only if they have the same invariants.
text: In fact, every abelian group is isomorphic to the ideal class group of some Dedekind domain.
text: Observe that by the Fundamental Theorem of Finitely Generated Abelian Groups, every abelian group A is isomorphic to a direct sum of a torsion subgroup and a torsion-free abelian group isomorphic to Z r {