Geodesic
The extraction of a~root in a~braid group
Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 405-416

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In this paper we construct an algorithm which recognizes for a given braid $A$ and a natural number $m$, whether there exists a braid $B$ such that $B^m=A$ in a braid group. Bibliography: 3 titles. 
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     author = {V. B. Styshnev},
     title = {The extraction of a~root in a~braid group},
     journal = {Izvestiya. Mathematics },
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     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a9/}
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V. B. Styshnev. The extraction of a~root in a~braid group. Izvestiya. Mathematics , Tome 13 (1979) no. 2, pp. 405-416. http://geodesic.mathdoc.fr/item/IM2_1979_13_2_a9/