Abstract commensurators of solvable Baumslag - Solitar groups

Details Abstract commensurators of solvable Baumslag - Solitar groups Abstract commensurators of solvable Baumslag - Solitar groups

2010-12-18

arxiv.org/abs/1012.4127v2

Mathematics

Group Theory

8 pages, no figure

Scientific paper

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 A_{11}=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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