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 Q of the rational numbers. This gives an explicit realization of the Higman embedding theorem for Q, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.
Belk, J., Hyde, J., Matucci, F. (2022). Embedding into a finitely presented group. BULLETIN (NEW SERIES) OF THE AMERICAN MATHEMATICAL SOCIETY, 59(4), 561-567 [10.1090/bull/1762].
Embedding into a finitely presented group
Matucci F.
Co-primo
2022
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 Q of the rational numbers. This gives an explicit realization of the Higman embedding theorem for Q, answering a Kourovka notebook question of Martin Bridson and Pierre de la Harpe.
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