Totally disconnected groups from baumslag-solitar groups

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Infinite Group Theory: From The Past To The Future, 2017, pp. 51 - 79
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© 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. For each Baumslag-Solitar group BS(m, n) (m, n σ Z \ (0)), a totally disconnected, locally compact group, Gm,n, is constructed so that BS(m, n) is identified with a dense subgroup of Gm,n. The scale function on Gm,n, a structural invariant for the topological group, is seen to distinguish the parameters m and n to the extent that the set of scale values is MathML Nff. It is also shown that Gm,n has flat rank 1 when |m| = |n| and 0 otherwise, and that Gm,n has a compact, open subgroup isomorphic to the product Q((Zp, +) | p is a prime divisor of the scale).
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