Abelianness is directed union-closed
This article gives the statement, and possibly proof, of a group property (i.e., Abelian group) satisfying a group metaproperty (i.e., directed union-closed group property)
View all group metaproperty satisfactions | View all group metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for group properties
Get more facts about Abelian group |Get facts that use property satisfaction of Abelian group | Get facts that use property satisfaction of Abelian group|Get more facts about directed union-closed group property
The union of any nonempty directed set of Abelian subgroups of a group is again Abelian.
The proof follows directly from facts (1) and (2).