On a Nonsingular Equation of Length 9 Over Torsion Free Groups

Authors

  • M. Fazeel Anwar Sukkur IBA University
  • Mairaj Bibi COMSATS University Islamabad
  • Muhammad Saeed Akram Khawaja Fareed UEIT

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i2.3405

Keywords:

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

Keywords:

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

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.

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How to Cite

Anwar, M. F., Bibi, M., & Akram, M. S. (2019). On a Nonsingular Equation of Length 9 Over Torsion Free Groups. European Journal of Pure and Applied Mathematics, 12(2), 590–604. https://doi.org/10.29020/nybg.ejpam.v12i2.3405