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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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/

[1] Artin E., Theorie der Zopf, Hamburg Abh., No 4, 47–72

[2] Garsaid F. L., “O gruppe kos i drugikh gruppakh”, Matematika, 14:4 (1970), 117–132

[3] Makanin G. S., “O normalizatorakh gruppy kos”, Matem. sb., 86(128):2(10) (1971), 171–179 | MR | Zbl