IRRATIONAL-SLOPE VERSIONS OF THOMPSON'S GROUPS T AND V

摘要

In this paper, we consider the T- and V -versions, T_τ and V_τ , of the irrational slope Thompson group F_τ considered in J. Burillo, B. Nucinkis and L. Reeves An irrational-slope Thompson's group, Publ. Mat. 65 (2021), 809–839. We give infinite presentations for these groups and show how they can be represented by tree-pair diagrams similar to those for T and V .We also show that Tτ and Vτ have index-2 normal subgroups, unlike their original Thompson counterparts T and V . These index-2 subgroups are shown to be simple.