#### Vol. 316, No. 1, 2022

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Divergence of finitely presented subgroups of CAT(0) groups

### Noel Brady and Hung Cong Tran

Vol. 316 (2022), No. 1, 1–52
##### Abstract

We construct families of $\mathrm{CAT}\left(0\right)$ groups containing finitely presented groups whose divergence functions are of the form ${r}^{\alpha }$ for a dense set of exponents $\alpha \in \left[2,\infty \right)$ and ${r}^{q}\mathrm{log}\left(r\right)$ for integers $q\ge 2$. The same construction also yields examples of $\mathrm{CAT}\left(0\right)$ groups containing contracting elements which are not contracting in certain finitely presented subgroups.

##### Keywords
group divergence, CAT(0) groups, contracting elements
##### Mathematical Subject Classification
Primary: 20F65, 20F67