Assertion: finite abelian group | /r/HasProperty | isomorphic
Facets:
value: to the four direct products
type: OTHER
Source sentences:
text: It turns out that an arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants.
text: It follows that any finite abelian group G {\displaystyle G} is isomorphic to a direct sum of the form
text: I know that each finite abelian group is isomorphic to a direct product of cyclic groups of prime orders $>
text: I understand that a finite abelian group of order 36 is indeed isomorphic to the four direct products that I have listed.
text: It seems to me that Hungerford's argument is that since a finite abelian group $G$ is isomorphic to the direct product of such cyclic subgroups, then it is only isomorphic to such cyclic subgroups.
text: An arbitrary finite abelian group is isomorphic to a direct sum of finite cyclic groups of prime power order, and these orders are uniquely determined, forming a complete system of invariants.