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arXiv · 2610.23637

Two-generator presentations with a relation gap

Laurent Bartholdi·Martin R. Bridson·Roman Mikhailov·John Nicholson
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Abstract

We exhibit two-generator two-relator group presentations that have cyclic relation modules but do not present one-relator groups; this resolves the relation gap problem. By attaching a single 3-cell to each of the corresponding presentation 2-complexes, one obtains counterexamples to Wall's D2 problem.

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Laurent Bartholdi, Martin R. Bridson, Roman Mikhailov, John Nicholson. 2026-10-16. Two-generator presentations with a relation gap. https://arxiv.org/abs/2610.23637

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