Set of Words Generates Group/Corollary

Corollary to Set of Words Generates Group

Let $G$ be a group.

Let $T \subseteq G$.

Let $\map W T$ be the set of words of $T$.

If $T$ is closed under taking inverses, then $\map W T$ is a subgroup of $G$.

Proof

This follows directly from Set of Words Generates Group and the fact that $T$ has the same properties as $\hat S$ in that result.

$\blacksquare$