Abstract commensurators of solvable Baumslag - Solitar groups

2010/12/18 by Oleg Bogopolski, Bogopolski, Oleg
Engineering · Mathematics · #20E36 #FOS: Mathematics #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras #graph theory and CDMA systems #math.GR #msc:20E36

paper · pdf · doi:10.48550/arxiv.1012.4127

8 pages, no figure

openalex publication_date 2010/12/18 · arxiv created 2011/03/03 · arxiv updated 2011/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that for any natural n>1, the abstract commensurator group of the Baumslag - Solitar group BS(1,n) is isomorphic to the group of 2 by 2 upper triangular matrices A over rational numbers with A₁₁=1. 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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