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arXiv · 2609.08863

Solvable groups defined by redundant cyclic presentations

Ihechukwu Chinyere
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Abstract

We study the two-generator one-relator groups defined by $\langle x_0,x_1\mid U(x_0,x_1)U(x_1,x_0)^{-1}\rangle$, and determine exactly which of them fail to contain a free subgroup of rank $2$. We show that every such group is a solvable Baumslag--Solitar group $BS(1,m)$, and that every integer value $m$ can occur. This disproves a conjecture predicting that only $m\in \{-1,0,1\}$ can occur.

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Ihechukwu Chinyere. 2026-09-08. Solvable groups defined by redundant cyclic presentations. https://arxiv.org/abs/2609.08863

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