On certain equations of arbitrary length over torsion-free groups

2019/03/15 by Anwar, M. Fazeel, Bibi, M., Iqbal, S.
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1903.07710

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.

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