Assertion: abelian group's subgroup | /r/HasProperty | generated by element
Facets:
Source sentences:
text: The second and third definition are equivalent because the subgroup generated by an element is precisely the set of its powers.
text: There is a unique infinite cyclic group, namely For any group and any element in it, we can consider the subgroup generated by that element.
text: The order of an element equals the order of the cyclic subgroup generated by this element.
text: Consider the subgroup of G generated by elements corresponding to (qi^(k_i1 - 1), 0) and (0, qi^(k_i2 - 1)) in this subgroup.