THOMPSON'S GROUP IS DISTORTED IN THE THOMPSON-STEIN GROUPS

摘要

We show that the inclusion map of the generalized Thompson groups F (n_i) is exponentially distorted in the Thompson—Stein groups F(n_l , . . . , n_k) for k > 1. One consequence is that F is exponentially distorted in F (n_1, . . . , n_k) for k > 1 whenever n_i = 2~m for some m (whenever noi, m exist such that n_i = 2~m, there is no obviously "natural" inclusion map of F into F (n_1, n_k)). This is the first known example in which the natural embedding of one of the Thompson-type groups into another is not quasi-isometric.