Timeline for The number of uniformly finite subgroups of some Lie groups
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4 events
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| Jun 9, 2020 at 7:24 | comment | added | YCor | It amounts to showing that for every finite group $F$ there are finitely many conjugacy classes of homomorphisms $F\to G$. This is a standard fact, at least in the OP's setting. For instance this is explicit in [D.H. Lee, T.S. Wu. On conjugacy of homomorphisms of topological groups. Illinois J. Math. 13 1969 694-699], but already follows from Weil's rigidity (1964), and was possibly known earlier. (For the general case: use conjugacy of maximal compact subgroups —due to Iwasawa— to reduce to the compact case.) | |
| Jun 9, 2020 at 4:56 | comment | added | Moishe Kohan | I am sure this was asked earlier; indeed, there are only finitely many finite subgroups of the given order in each connected Lie group up to conjugation. | |
| Jun 9, 2020 at 0:55 | comment | added | user158834 | See this question: mathoverflow.net/questions/17072/the-finite-subgroups-of-sun | |
| Jun 8, 2020 at 23:28 | history | asked | Totoro | CC BY-SA 4.0 |