Abstract
We prove that for any n ≥ 2, the abstract commensurator group of the Baumslag–Solitar group BS(1, n) is isomorphic to the subgroup of GL2(ℚ). We also prove that for any finitely generated group G with the unique root property the natural homomorphisms Aut(G) → Comm(G) → QI(G) are embeddings.
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