Timeline for Large subgroups of Knuth's non-associative "group" on ${\cal P}(\mathbb{N})$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 16, 2023 at 14:17 | comment | added | Dominic van der Zypen | Beautiful, thanks @bof! | |
| Dec 15, 2023 at 2:54 | comment | added | bof | I've rewritten my answer to be (I hope) more readable. By the way, there's no need to call the magma $(\mathcal P(\mathbb N),\oplus)$ a "group" in scare quotes; the standard name for such an object is loop. If you extend the operation to $\mathcal P(\mathbb Z)$, the magma $(\mathcal P(\mathbb Z),\oplus)$ is not a loop or a quasigroup, and it still has no nontrivial "subgroups", but it has a (slightly) nontrivial "subsemigroup", namely $\{\emptyset,\mathbb Z\}$. | |
| Dec 14, 2023 at 12:24 | vote | accept | Dominic van der Zypen | ||
| Dec 14, 2023 at 10:36 | review | Close votes | |||
| Dec 20, 2023 at 3:02 | |||||
| Dec 14, 2023 at 3:47 | answer | added | bof | timeline score: 9 | |
| Dec 12, 2023 at 21:55 | comment | added | Achim Krause | Note: Already $(A+A)+(A+A) = (A+(A+(A+A)))$ seems to put strong constraints on the elements such a subgroup may contain, there might be very few. | |
| Dec 12, 2023 at 21:20 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |