Embedding ℚ into a finitely presented group

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