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The \(n\)th root of a braid is unique up to conjugacy. (English) Zbl 1063.20041
The author proves a conjecture due to Makanin: if \(\alpha\) and \(\beta\) are elements of the Artin braid group \(B_n\) such that \(\alpha^k=\beta^k\) for some nonzero integer \(k\), then \(\alpha\) and \(\beta\) are conjugate. The proof involves the Nielsen-Thurston classification of braids.

MSC:
20F36 Braid groups; Artin groups
20F65 Geometric group theory
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