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arXiv · 2304.07656

Constraint stability in permutations and action traces

Goulnara Arzhantseva·Liviu Paunescu
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Abstract

An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We extend such a characterisation to constraint stability. We give sufficient conditions for a group to be constraint stable. As an application, we obtain many new examples of groups stable in permutations, in particular, among free amalgamated products over a finite group. This is the first general result (besides trivial case of free products) which gives a wealth of non-amenable groups stable in permutations.

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Goulnara Arzhantseva, Liviu Paunescu. 2024-12-12. Constraint stability in permutations and action traces. https://arxiv.org/abs/2304.07656

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