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The descent method for equations over groups. (English. Russian original) Zbl 0914.20024
Mosc. Univ. Math. Bull. 50, No. 4, 56-58 (1995); translation from Vestn. Mosk. Univ., Ser. I 1995, No. 4, 90-93 (1995).
A new class of equations \(r(t)=1\) solvable over a torsion-free group is obtained. This class contains, for example, all equations of the form \(a_1ta_2t\cdots a_mtb_1t^{-1}b_2t^{-1}\cdots b_kt^{-1}=1\).

MSC:
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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