Totally disconnected groups from baumslag-solitar groups

Elder, M; Willis, G

Totally disconnected groups from baumslag-solitar groups

Elder, M

Willis, G

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Publication Type:: Chapter
Citation:: Infinite Group Theory: From The Past To The Future, 2017, pp. 51 - 79
Issue Date:: 2017-12-26

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	Willis, G	en_US
dc.date.issued	2017-12-26	en_US
dc.identifier.citation	Infinite Group Theory: From The Past To The Future, 2017, pp. 51 - 79	en_US
dc.identifier.isbn	9789813204041	en_US
dc.identifier.uri	http://hdl.handle.net/10453/129387
dc.description.abstract	© 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).	en_US
dc.relation.ispartof	Infinite Group Theory: From The Past To The Future	en_US
dc.title	Totally disconnected groups from baumslag-solitar groups	en_US
dc.type	Chapter
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US

Abstract:

© 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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http://hdl.handle.net/10453/129387