Characteristically complemented characteristic is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., characteristically complemented characteristic subgroup) 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 characteristically complemented characteristic subgroup |Get facts that use property satisfaction of characteristically complemented characteristic subgroup | Get facts that use property satisfaction of characteristically complemented characteristic subgroup|Get more facts about transitive subgroup property


Statement

Statement with symbols

Suppose are groups such that is a characteristically complemented characteristic subgroup of and is a characteristically complemented characteristic subgroup of . Then, is a characteristically complemented characteristic subgroup of .

Related facts

Similar facts

Opposite facts

Facts used

  1. Characteristicity is transitive
  2. Characteristicity is strongly join-closed