# Direct factor is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., direct factor) satisfying a subgroup metaproperty (i.e., transitive subgroup property)

View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties

Get more facts about direct factor |Get facts that use property satisfaction of direct factor | Get facts that use property satisfaction of direct factor|Get more facts about transitive subgroup property

## Statement

Suppose is a group and . Suppose that is a direct factor of and is a direct factor of . Then, is a direct factor of .