Assertion: abelian group's subgroup | /r/HasProperty | finite
Facets:
value: in an infinite 2-group
type: OTHER
value: in such a group
type: OTHER
Source sentences:
text: In particular, in such a group all Abelian subgroups are finite, the group also satisfies the condition of minimality for Abelian subgroups.
text: If some maximal elementary Abelian subgroup is finite in an infinite 2-group, then the group itself is a finite extension of the direct product of the finite number of quasi-cyclic groups.
text: A group such that every finitely generated subgroup is finite is called locally finite.
text: every discrete subgroup of a compact Hausdorff group is finite.