# Homomorph-containment is finite direct power-closed

From Groupprops

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

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## Statement

Suppose is a homomorph-containing subgroup of a group . Let be a natural number. Then, in the direct power of (i.e., the external direct product of with itself times) the corresponding subgroup is a homomorph-containing subgroup.