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1.18 (1965)

Solved

a) Does there exist an algorithm for determining the solubility of equations in a free group?
b) Describe the structure of all solutions of an equation when it has at least one solution.

Contributor: Yu. L. Ershov

Progress

a) Yes, there does (G. S. Makanin, Math. USSR–Izv., 21 (1982), 546–582; 25 (1985), 75–88).
b) This was described (A. A. Razborov, Math. USSR–Izv., 25 (1984), 115–162).

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