Assertion: abelian group's element | /r/HasAspect | infinite order
Facets:
Source sentences:
text: An abelian group is called torsion-free if every non-zero element has infinite order.
text: the element xy is a product of two torsion elements, but has infinite order.
text: A torsion-free abelian group of rank 1 is an abelian group such that every element except the identity has infinite order, and for any two non-identity elements a and b
text: On the other hand, any nontrivial finite group cannot be free, since the elements of a free generating set of a free group have infinite order.