Assertion: finite abelian group | /r/HasProperty | $g$
Facets:
Source sentences:
text: If $m$ divides the order of a finite Abelian group $G$, then $G$ has a subgroup of order $m$.
text: Every finite abelian group $G$ is the direct sum of cyclic groups, each of prime power order",
text: A finite abelian group $G$ can be written as the direct product of p-groups $G(p_1) \times
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.