Group Theory/Free products and amalgamated sums

Note that when $$n$$ is odd, then the reduced word obtained in this way will not be the empty tuple. Otherwise, the empty tuple may result.

Exercises

 * 1) Prove that when $$S$$ is a set such that $$|S| \ge 2$$, then $$F \langle S \rangle$$ is not an abelian group.