On a theorem of Avez

Elder, M; Rogers, C

On a theorem of Avez

Elder, M

Rogers, C

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Publication Type:: Journal Article
Citation:: Journal of Group Theory, 2019, 22 (3), pp. 383 - 395
Issue Date:: 2019-05-01

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Field	Value	Language
dc.contributor.author	Elder, M https://orcid.org/0000-0002-2438-3945	en_US
dc.contributor.author	Rogers, C	en_US
dc.date.available	2020-05-25T19:04:52Z
dc.date.issued	2019-05-01	en_US
dc.identifier.citation	Journal of Group Theory, 2019, 22 (3), pp. 383 - 395	en_US
dc.identifier.issn	1433-5883	en_US
dc.identifier.uri	http://hdl.handle.net/10453/129666
dc.description.abstract	© de Gruyter 2019. For each symmetric, aperiodic probability measure on a finitely generated group G, we define a subset A consisting of group elements g for which the limit of the ratio n.g/=n.e/ tends to 1. We prove that A is a subgroup, is amenable, contains every finite normal subgroup, and G D A if and only if G is amenable. For non-amenable groups we show that A is not always a normal subgroup and can depend on the measure. We formulate some conjectures relating A to the amenable radical.	en_US
dc.relation.ispartof	Journal of Group Theory	en_US
dc.relation.isbasedon	10.1515/jgth-2018-0042	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	On a theorem of Avez	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	22	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0802 Computation Theory and 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	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	22	en_US

Abstract:

© de Gruyter 2019. For each symmetric, aperiodic probability measure on a finitely generated group G, we define a subset A consisting of group elements g for which the limit of the ratio n.g/=n.e/ tends to 1. We prove that A is a subgroup, is amenable, contains every finite normal subgroup, and G D A if and only if G is amenable. For non-amenable groups we show that A is not always a normal subgroup and can depend on the measure. We formulate some conjectures relating A to the amenable radical.

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http://hdl.handle.net/10453/129666