# Full invariance is finite direct power-closed

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., fully invariant subgroup) satisfying a subgroup metaproperty (i.e., finite direct power-closed 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 fully invariant subgroup |Get facts that use property satisfaction of fully invariant subgroup | Get facts that use property satisfaction of fully invariant subgroup|Get more facts about finite direct power-closed subgroup property

## Contents

## Statement

### Statement with symbols

Suppose is a fully invariant subgroup of a group . For any positive integer , consider the external direct product of with itself , and denote this by . Let be the subgroup comprising those elements where all coordinates are from within . Then, is a fully invariant subgroup of .