Geodesic
An Equation in a Free Group Defining Pure Braids
Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 591-602 
G. S. Makanin; A. G. Savushkina. An Equation in a Free Group Defining Pure Braids. Matematičeskie zametki, Tome 70 (2001) no. 4, pp. 591-602. http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a10/
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     author = {G. S. Makanin and A. G. Savushkina},
     title = {An {Equation} in a {Free} {Group} {Defining} {Pure} {Braids}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_70_4_a10/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A description of the general solution of the equation $$ x_1^{-1}a_1x_1x_2^{-1}a_2x_2\dots x_n^{-1}a_nx_n =a_1a_2\dots a_n $$ in a free group is given.

[1] Burau W., “Über Zopfinvarianten”, Abh. Math. Semin. Univ. Hamburg, 9 (1933), 117–124 | DOI

[2] Markov A. A., “Osnovy algebraicheskoi teorii kos”, Tr. MIAN, 16, Izd-vo Akademii nauk SSSR, M.–L., 1945, 3–53 | MR | Zbl

[3] Artin E., “Theory of braids”, Ann. Math., 48 (1947), 101–126 | DOI | MR | Zbl

[4] Magnus V., Karras A., Soliter D., Kombinatornaya teoriya grupp, Nauka, M., 1974 | Zbl

[5] Birman J., “Braids, Links, Mapping Class Groups”, Ann. Math. Stud., 82, Princeton Univ. Press, Princeton, 1975 | Zbl

[6] Makanina A. G., “Opredelyayuschie sootnosheniya gruppy krashenykh kos”, Vestn. MGU. Ser. 1. Matem., mekh., 1992, no. 3, 14–19 | MR | Zbl