Assertion: abelian group's subgroup | /r/HasProperty | central
Facets:
value: for an odd-order group
type: TRANSITIVE-OBJECT
Source sentences:
text: Since every central subgroup is normal, it follows that every minimal normal subgroup of a finite p-group is central and has order
text: However, for an odd-order group, any normal subgroup of order three is central.
text: This follows from a more general fact: a normal subgroup whose order is the least prime divisor of the order of the group is central.
text: It is also true that a normal subgroup of order two is central.
text: More generally, it is true that a normal subgroup whose order is the least prime divisor of the order of the group is central.
text: In fact, a normal subgroup whose order is the smallest prime dividing the order of the group, must be central.