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arXiv · 2403.07374

Free submonoids of hyperbolic monoids

Matthias Hamann
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Abstract

In this paper, we prove that infinite cancellative finitely generated hyperbolic monoids never contain $\mathbb N\times\mathbb N$ as a submonoid but that they contain an element of infinite order and, if they are elementary, then they also contain a free monoid of rank at least 2. As a corollary we obtain that the latter have exponential growth. We prove these results by analysing the monoid of self-embeddings of hyperbolic digraphs and proving fixed-point theorems for them.

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Matthias Hamann. 2024-03-12. Free submonoids of hyperbolic monoids. https://arxiv.org/abs/2403.07374

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