Letizia Issini | Searcharxiv

arXiv2026

Period growth and co-context-free groups

We study period growth in co-context-free groups, giving general results and looking at specific examples such as Thompson groups $T$ and $V$ and the Houghton groups $H_m$. Along the way, we give a refined upper bound on the word metric in Thompson $V$, as well as efficient algorithms to determine if elements of $V$ are torsion, and compute their order. We also adapt our algorithm to compute the rotation number of elements of $T$ and answer a question of D. Calegari.

math.GR↗

arXiv2023

On linear divergence in finitely generated groups

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.

math.GR↗