Equations in a free Q-group

Details Equations in a free Q-group Equations in a free Q-group

1996-05-13

arxiv.org/abs/math/9605204v1

Mathematics

Group Theory

LaTex file, 26 pages. Not avilable

Scientific paper

In this work we investigate tensor completions of groups by associative rings, which were introduced by R.Lyndon and G.Baumslag in 1960s. The main result states that there exists an algorithm that decides if a given finite system of equations over a free ${\bf Q}$-group has a solution, and if it does, finds a solution. This statement can be generalized for ${\bf Q}$-completions of torsion-free hyperbolic groups. Our proof significantly uses the techniques of word hyperbolic groups and the results of E.Rips and Z.Sela on the solvability of systems of equations in hyperbolic groups.

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