On proper powers in free products and Dehn surgery (Q1105695)

The author proves the following theorem: (which was also proved independently by Baumslag, Morgan and Shalen). Let p, q and r be integers greater than or equal to 2, then for any word \(w\in {\mathbb{Z}}/p*{\mathbb{Z}}/q\) \(({\mathbb{Z}}/p*{\mathbb{Z}}/q)/<\omega\) \(r>\not\cong \{e\}\). (Here, the symbol `*' denotes the free product operation between groups and `\(<\omega\) \(r>'\) denotes the normal closure of \(\omega\) r in \({\mathbb{Z}}/p*{\mathbb{Z}}/q.)\) There are some interesting topological applications to knot theory and Dehn surgery.