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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
##### Keywords:
braid groups; unique roots; conjugacy; Nielsen-Thurston theory
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##### References:
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