Timeline for Examples of amenable, Hausdorff, locally compact, second countable groups which are not discrete, not compact, and not abelian
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2023 at 7:51 | comment | added | mathemagician99 | The Heisenberg group is a locally compact, non-compact, second-countable, amenable, non-Abelian group. | |
| Apr 7, 2023 at 20:20 | comment | added | Yemon Choi | Since there are amenable Lie groups which are not unimodular (immediately implying that they cannot be written as discrete times compact times abelian) I can answer the question in your title but this appears not to be what you want. It would help people if you made precise the "additional requirements" | |
| Apr 6, 2023 at 0:44 | comment | added | YCor | Maybe try to ask a question for which some obvious constructions such as direct product doesn't produce obvious examples. | |
| Apr 6, 2023 at 0:32 | comment | added | Gerald Edgar | Any group acts on itself. What about $S_3 \oplus \mathbb R$, where $S_3$ is not abelian and $\mathbb R$ is not compact and not discrete ? I don't know if there are "plenty" of elements as described, however. | |
| Apr 5, 2023 at 22:55 | history | asked | Jacob R | CC BY-SA 4.0 |