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On the abstract commensurator of Baumslag–Solitar groups



commensurator of G, or, for brevity, the commensurator of G, and denote it by Comm(G). Baumslag–Solitar groups [1] are given by the presentation BS(p, q) = a, t | t−1 ap t = aq . Let Hm be a group given by the presentation Hm = c1 , c2 , . . . , cm , d | d−1 cp d = cq , cq = cp , i = 1, 2, . . . , m − 1 . m i 1 i+1 If p and q are coprime and are distinct from 1, −1, and 0 then any subgroup of finite index in BS(p, q) is isomorphic to one of Hm (see [2]). Supported by RFBR (project No. 10-01-00391), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-3669.2010.1), by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No., and by the Federal Program “Scientific and Scientific-Pedagogical Cadres of Innovative Russia” (gov. contract No. 14.740.11.0346). ∗ UDC 512.543 Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Koptyuga 4, Novosibirsk, 630090



Algebra and LogicSpringer Journals

Published: May 1, 2011

DOI: 10.1007/s10469-011-9132-y

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