Solving singular equations of length eight over torsion-free groups

Mairaj Bibi; Sajid Ali; Muhammad Shoaib Arif; Kamaleldin Abodayeh; Mairaj Bibi; Sajid Ali; Muhammad Shoaib Arif; Kamaleldin Abodayeh

doi:10.3934/math.2023324

AIMS Mathematics

2023, Volume 8, Issue 3: 6407-6431. doi: 10.3934/math.2023324

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Research article

Solving singular equations of length eight over torsion-free groups

1.
Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad, 45550, Pakistan
2.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3.
Department of Mathematics, Air University, PAF Complex E-9, Islamabad, 44000, Pakistan

Received: 16 April 2022 Revised: 31 July 2022 Accepted: 11 August 2022 Published: 03 January 2023
MSC : 20F70, 20F05, 20E06, 20F06

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.
- torsion free group,
- relative presentation,
- star graph,
- weight test
Citation: Mairaj Bibi, Sajid Ali, Muhammad Shoaib Arif, Kamaleldin Abodayeh. Solving singular equations of length eight over torsion-free groups[J]. AIMS Mathematics, 2023, 8(3): 6407-6431. doi: 10.3934/math.2023324

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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.

References

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