2024/03/12 by Hamann, Matthias
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2403.07374
In this paper, we prove that infinite cancellative finitely generated hyperbolic monoids never contain \mathbb N×\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.