Length functions on groups and rigidity

Shengkui Ye

Let $G$ be a group. A function $l:G\to [0,\infty )$ is called a length function if (1) $l(g^n)=|n|l(g)$ for any $g\in G$ and $n\in \mathbb{Z};$ (2) $l(hgh^{-1})=l(…