Embedding $\mathbb{Q}$ into a Finitely Presented Group

Abstract

We observe that the group of all lifts of elements of Thompson's group $T$ to the real line is finitely presented and contains the additive group $\mathbb{Q}$ of the rational numbers. This gives an explicit realization of the Higman embedding theorem for $\mathbb{Q}$, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.

arXiv comment7 pages, no figures; to appear in $\text{Bulletin of the American Mathematical Society}$. This version contains only the embedding of $\mathbb{Q}$ into the group of all lifts of elements of Thompson's group $T$ to the real line. The discussion of the group $T\mathcal{A}$ will appear elsewhere