It is a consequence of Higman's embedding theorem that the additive group $\mathbb{Q}$ of rational numbers can be embedded into a finitely presented group. Though Higman's proof is constructive, the resulting group presentation would be very large and unpleasant. In 1999, Martin Bridson and Pierre de la Harpe asked for an explicit and "natural" example of a finitely presented group that contains an embedded copy of $\mathbb{Q}$. In this talk, we describe some solutions to the Bridson - de la Harpe problem related to Richard Thompson's groups $F$, $T$, and $V$. Moreover, we prove that there exists a group containing $\mathbb{Q}$ which is simple and has type $F$ infinity. This is joint work with Jim Belk and James Hyde.