Embedding $\mathbb{Q}$ into a Finitely Presented Group
Group Theory
2022-03-29 v4
Abstract
We observe that the group of all lifts of elements of Thompson's group to the real line is finitely presented and contains the additive group of the rational numbers. This gives an explicit realization of the Higman embedding theorem for , answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.
Cite
@article{arxiv.2005.02036,
title = {Embedding $\mathbb{Q}$ into a Finitely Presented Group},
author = {James Belk and James Hyde and Francesco Matucci},
journal= {arXiv preprint arXiv:2005.02036},
year = {2022}
}
Comments
7 pages, no figures; to appear in $\textit{Bulletin of the American Mathematical Society}$. 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