Conjugacy class conditions in locally compact second countable groups

Wesolek, Phillip

doi:10.1090/proc/12645

Conjugacy class conditions in locally compact second countable groups
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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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