On a Nonsingular Equation of Length 9 Over Torsion Free Groups

M. Fazeel Anwar, Mairaj Bibi, Muhammad Saeed Akram

Abstract

In \cite{levin}, Levin conjectured that every equation is solvable over a torsion free group. In this paper we consider a nonsingular equation $g_{1}tg_{2}t g_{3}t g_{4} t g_{5} t g_{6} t^{-1} g_{7} t g_{8}t \\ g_{9}t^{-1} = 1$ of length $9$ and show that it is solvable over torsion free groups modulo some exceptional cases.

Keywords

Asphericity; relative group presentations; torsion-free groups; group equations.

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