Divergence Property of the Brown-Thompson Groups and Braided Thompson Groups

Golan and Sapir proved that Thompson’s groups F, T and V have linear divergence. In the current paper, we focus on the divergence property of several generalisations of the Thompson groups. We first consider the Brown-Thompson groups \(F_n\) $F_n$ , \(T_n\) $T_n$ and \(V_n\) $V_n$ (also called Brown-Higman-Thompson group in some other context) and find that these groups also have linear divergence functions. We then focus on the braided Thompson groups BF,  \(\widehat{BF}\) $\widehat{\mathit{BF}}$ and \(\widehat{BV}\) $\widehat{\mathit{BV}}$ and prove that these groups have linear divergence. The case of BV has also been done independently by Kodama.