On linear divergence in finitely generated groups

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. Finally, we show that wreath products of graphs and Diestel-Leader graphs have linear divergence.