Geodesic
Equations in a~free group
Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 483-546.

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An algorithm for recognizing the solvability of arbitrary equations in a free group is constructed. Bibliography: 11 titles. 
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G. S. Makanin. Equations in a~free group. Izvestiya. Mathematics , Tome 21 (1983) no. 3, pp. 483-546. http://geodesic.mathdoc.fr/item/IM2_1983_21_3_a4/

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