1996/05/13 by Olga Kharlampovich, Kharlampovich, Olga, Alexey Myasnikov +1
Mathematics · #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR
paper · pdf · doi:10.48550/arxiv.math/9605204
LaTex file, 26 pages. Not avilable
arxiv created 1996/05/13 · openalex publication_date 1996/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.