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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Conjugacy class conditions in locally compact second countable groups
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by Phillip Wesolek PDF
Proc. Amer. Math. Soc. 144 (2016), 399-409 Request permission

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
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 399-409
  • MSC (2010): Primary 22D05, 03E15
  • DOI: https://doi.org/10.1090/proc/12645
  • MathSciNet review: 3415606