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arXiv · 2604.14903

Groups with arbitrarily poor permutation stability

Henry Bradford
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Abstract

We propose a quantitative notion of permutation stability for finitely generated groups. Our notion is related to, but distinct from, the ``stability rate'' introduced by Becker and Mosheiff (which is valid within the class of finitely presented groups). We construct a family of finitely generated stable groups which exhibit, quantitatively, arbitrarily ``bad'' permutation stability. This means that any application of a ``sample-and-substitute'' algorithm will be very slow in ascertaining whether a given tuple of permutations satisfy the defining relations of our groups.

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Henry Bradford. 2026-04-16. Groups with arbitrarily poor permutation stability. https://arxiv.org/abs/2604.14903

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