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arXiv · 2311.12938

On linear divergence in finitely generated groups

Letizia Issini
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Abstract

In this paper, we show that wreath products of groups have linear divergence, and we generalise the argument to permutational wreath products. We also prove that Houghton groups $\mathcal{H}_m$ with $m\geq 2$ and Baumslag-Solitar groups have linear divergence. We explain how to generalise the argument for wreath products so that it holds for halo products of groups whose halo is large-scale commutative. Finally, we show that wreath products of graphs and Diestel-Leader graphs have linear divergence. The argument for Diestel-Leader graphs is further generalised to horocyclic products of proper, geodesically complete, Busemann $\delta$-hyperbolic spaces that are uniformly not a quasi-line.

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Letizia Issini. 2023-11-21. On linear divergence in finitely generated groups. https://arxiv.org/abs/2311.12938

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