Assertion: abelian group's subgroup | /r/HasProperty | generated
Facets:
value: finitely
type: DEGREE
value: always
type: DEGREE
Source sentences:
text: A subgroup of finite index in a finitely generated group is always finitely generated, and the Schreier index formula gives a bound on the number of generators required.
text: The lattice of subgroups of a group satisfies the ascending chain condition if and only if all subgroups of the group are finitely generated.