On certain equations of arbitrary length over torsion-free groups

M. Fazeel Anwar; M. Bibi; S. Iqbal

On certain equations of arbitrary length over torsion-free groups

Group Theory 2023-10-10 v2 Geometric Topology

Authors: M. Fazeel Anwar , M. Bibi , S. Iqbal

Abstract

Let $G$ be a non-trivial torsion free group and $t$ be an unknown. In this paper we consider three equations (over $G$ ) of arbitrary length and show that they have a solution (over $G$ ) provided two relations among their coefficients hold. Such equations appear for all lengths greater than or equal to eight and the results presented in this article can substantially simplify their solution.

Keywords

torsion-free groups equations over groups group coefficients solvable equations arbitrary length

Cite

@article{arxiv.1903.07710,
  title  = {On certain equations of arbitrary length over torsion-free groups},
  author = {M. Fazeel Anwar and M. Bibi and S. Iqbal},
  journal= {arXiv preprint arXiv:1903.07710},
  year   = {2023}
}

Comments

Error found in one of the main theorems

On certain equations of arbitrary length over torsion-free groups

Abstract

Keywords

Cite

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