Timeline for Amenable automatic groups
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2021 at 7:49 | comment | added | HJRW | The Tits alternative for automatic groups seems to be an open problem. (See eg here: automaticgroups.tumblr.com.) Your question is very similar, and so is surely open too. | |
| May 24, 2021 at 18:50 | comment | added | Benjamin Steinberg | @Zaremsky If you can show automaticity of the bigger group would give the Grigorchuk group a rational crosssection you could eliminate that possibility. Or the Dehn function is likely to big. | |
| May 24, 2021 at 16:10 | comment | added | Matt Zaremsky | @BenjaminSteinberg yeah the only example I know of is due to Grigorchuk (iopscience.iop.org/article/10.1070/SM1998v189n01ABEH000293), I think by modifying "the" Grigorchuk group to be fin. pres. But I doubt anyone thinks it's automatic. | |
| May 24, 2021 at 12:47 | comment | added | Benjamin Steinberg | Most amenable but not elementary amenable groups I know are not finitely presented. But I'm no expert | |
| May 24, 2021 at 12:40 | comment | added | Derek Holt | The solvable Baumslag-Solitar groups ${\rm BS}(1,n)$ are however asynchronously automatic (meaning that the multiplier automata can read their two input tapes at different rates), while not being automatic. | |
| May 24, 2021 at 12:14 | comment | added | Matt Zaremsky | Good point about solvable groups; if it's even true that elementary amenable plus automatic implies virtually abelian, then probably there is no hope for known examples, since non-elementarily amenable groups are already quite hard to come by. | |
| May 24, 2021 at 11:41 | comment | added | Derek Holt | I suspect the answer is no. Note that (finitely generated) solvable groups are not automatic except when they are virtually abelian. | |
| May 24, 2021 at 11:16 | history | asked | Matt Zaremsky | CC BY-SA 4.0 |