Assertion: abelian group's element | /r/HasAspect | finite order
Facets:
value: by definition
type: OTHER
Source sentences:
text: Is it possible that each element of an infinite group has a finite order?
text: An abelian group is called periodic or torsion, if every element has finite order.
text: Every p-group is periodic since by definition every element has finite order.
text: A is the subgroup of A consisting of all elements that have finite order (the torsion elements of A).
text: An abelian group A is called a torsion (or periodic) group if every element of A has finite order and is called torsion-free if every element of A except the identity is of infinite order.
text: The torsion subgroup of an abelian group A is the subgroup of A consisting of all elements that have finite order.
text: Every locally finite group is periodic, i.e., every element has finite order.
text: That is, the only element of $G$ that has finite order is the identity element.
text: Since each element of $T(A)$ has finite order by definition, there exists a positive integer
text: We have proved that any element of $G=A/T(A)$ that has finite order is the identity,