# Verbality is strongly join-closed

From Groupprops

This article gives the statement, and possibly proof, of a subgroup property (i.e., verbal subgroup) satisfying a subgroup metaproperty (i.e., strongly join-closed subgroup property)

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## Statement

Suppose is a group and are verbal subgroups of . Then, the join of subgroups is also a verbal subgroup of .

## Related facts

## Proof

We simply look at the sets of words for each , and take the set of products of all such words.