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arXiv · 2507.06599

Minimal sofic shift on a group that is not finitely-generated

Ville Salo
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Abstract

We prove that there exists a group which is not finitely generated, but admits a minimal sofic shift. This answers a question of Doucha, Melleray and Tsankov. The group is of the form $(F_4 \times F_2) \rtimes F_{\infty}$. The construction itself is based on simulation theory and properties of Thompson's~$V$.

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Ville Salo. 2025-07-09. Minimal sofic shift on a group that is not finitely-generated. https://arxiv.org/abs/2507.06599

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