# Finite direct power-closed characteristic is transitive

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., finite direct power-closed characteristic subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)

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## Statement

### Statement with symbols

Suppose are groups such that is a finite direct power-closed characteristic subgroup of and is a finite direct power-closed characteristic subgroup of . Then, is a finite direct power-closed characteristic subgroup of .