Totally disconnected groups from Baumslag-Solitar groups

Title: Totally disconnected groups from Baumslag-Solitar groups
Creator: Elder, Murray; Willis, George
Relation: ARC.DP0984342 http://purl.org/au-research/grants/arc/DP0984342 & DP120100996 http://purl.org/au-research/grants/arc/DP120100996 & FT110100178 http://purl.org/au-research/grants/arc/FT110100178
Relation: Infinite Group Theory: From The Past To The Future p. 51-79
Publisher Link: http://dx.doi.org/10.1142/9789813204058_0004
Publisher: World Scientific Publishing
Resource Type: book chapter
Date: 2018
Description: For each Baumslag-Solitar group BS(m, n) (m, n ∈ 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 {(lcm(m,n)/|m|)^ρ, (lcm(m,n)/|n|)^ρ | ρ∈N}. 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).
Subject: totally disconnected locally compact group; commensurated subgroup; Baumslag-Solitar group; scale; minimizing subgroup; flat rank
Identifier: http://hdl.handle.net/1959.13/1442986
Identifier: uon:41852
Identifier: ISBN:9789813204041
Language: eng