@article{Bibi2023, 
author = {Mairaj Bibi and Sajid Ali and Muhammad Shoaib Arif and Kamaleldin Abodayeh},
title = {Solving singular equations of length eight over torsion-free groups},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6407-6431},
keywords = {torsion free group, relative presentation, star graph, weight test},
url = {https://www.sciopen.com/article/10.3934/math.2023324},
doi = {10.3934/math.2023324},
abstract = {It was demonstrated by Bibi and Edjvet in [1] that any equation with a length of at most seven over torsion-free group can be solvable. This corroborates Levin's [2] assertion that any equation over a torsion-free group is solvable. It is demonstrated in this article that a singular equation of length eight over torsion-free groups is solvable.}
}