Assertion: abelian group's subgroup | /r/HasProperty | cyclic
Facets:
value: virtually
type: MANNER
value: more generally
type: DEGREE
value: by definition
type: OTHER
Source sentences:
text: The generalized quaternion groups have the property that every abelian subgroup is cyclic.
text: That subgroup is, by definition, a cyclic group.
text: Sign representations with i,j,k-kernel: Q 8 has three maximal normal subgroups: the cyclic subgroups generated by i, j, and k respectively.
text: A subgroup of a cyclic group is cyclic.
text: p. More generally, every finite subgroup of the multiplicative group of any field is cyclic.
text: All subgroups and quotient groups of cyclic groups are cyclic.
text: finite index n. Every abelian subgroup of a Gromov hyperbolic group is virtually cyclic.
text: Every finite subgroup of a cyclically ordered group is cyclic.
text: In general, subgroups of cyclic groups are also cyclic.
text: Then H must be cyclic (all subgroups of cyclic groups are cyclic).
text: This follows from the more general fact that any finite subgroup of the multiplicative group of a field is cyclic.
text: Further information: finite subgroup of multiplicative group of field is cyclic
text: A necessary and sufficient criterion for a d-periodic cohomology is that the only abelian subgroups of G are cyclic.