Divergence of finitely presented groups (Q2076075)

Summary: We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form \(r^{\alpha}\) for a dense set of exponents \(\alpha \in [2,\infty)\) and \(r^n \log (r)\) for integers \(n \geq 2\). The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.