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

Abstract

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 \(F_n\), \(T_n\) and \(V_n\) (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, \(\widehat{BF}\) and \(\widehat{BV}\) and prove that these groups have linear divergence. The case of BV has also been done independently by Kodama.