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Conjugacy class conditions in locally compact second countable groups


Author: Phillip Wesolek
Journal: Proc. Amer. Math. Soc. 144 (2016), 399-409
MSC (2010): Primary 22D05, 03E15
DOI: https://doi.org/10.1090/proc/12645
Published electronically: August 18, 2015
MathSciNet review: 3415606
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Abstract: Many non-locally compact second countable groups admit a comeagre conjugacy class. For example, this is the case for $ S_{\infty }$, $ Aut(\mathbb{Q},<)$, and, less trivially, $ Aut(\mathcal {R})$ for $ \mathcal {R}$ the random graph. A. Kechris and C. Rosendal ask if a non-trivial locally compact second countable group can admit a comeagre conjugacy class. We answer the question in the negative via an analysis of locally compact second countable groups with topological conditions on a conjugacy class.


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Additional Information

Phillip Wesolek
Affiliation: Université Catholique de Louvain, Institut de Recherche en Mathématiques et Physique (IRMP), Chemin du Cyclotron 2, box L7.01.02, 1348 Louvain-la-Neuve, Belgique
Email: phillip.wesolek@uclouvain.be

DOI: https://doi.org/10.1090/proc/12645
Keywords: Totally disconnected locally compact groups, profinite groups, comeagre conjugacy class
Received by editor(s): November 25, 2013
Received by editor(s) in revised form: September 17, 2014
Published electronically: August 18, 2015
Communicated by: Mirna Dzamonja
Article copyright: © Copyright 2015 American Mathematical Society