Assertion: abelian group's subgroup | /r/HasProperty | characteristic
Facets:
value: certainly
type: MANNER
value: strictly
type: DEGREE
value: fully
type: DEGREE
value: more generally
type: DEGREE
value: always
type: DEGREE
Source sentences:
text: Since the derived subgroup is characteristic, any automorphism of G induces an automorphism of the abelianization.
text: The subgroups of type (1), (2), (4) and (6) are characteristic.
text: However, not every normal subgroup is characteristic.
text: However, the subgroup, {1, −1} , is characteristic, since it is the only subgroup of order 2.
text: More generally, any verbal subgroup is always fully characteristic.
text: Similarly, while being strictly characteristic (distinguished) is not transitive, it is true that every fully characteristic subgroup of a strictly characteristic subgroup is strictly characteristic.
text: Every subgroup that is fully characteristic is certainly strictly characteristic and characteristic; but
text: Every subgroup that is fully characteristic is certainly strictly characteristic and characteristic; but
text: Every subgroup that is fully characteristic is certainly strictly characteristic and characteristic; but
text: Every subgroup of a cyclic group is characteristic.