Timeline for Can one characterize amenable groups with $C_G(x)$ cyclic for all $x\neq 1$?
Current License: CC BY-SA 3.0
9 events
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| May 7, 2013 at 14:20 | history | edited | Lee Mosher |
edited tags
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| Apr 27, 2013 at 5:19 | history | edited | Arturo Magidin | CC BY-SA 3.0 |
make the body self-contained, make title less prone to misreading
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| Apr 27, 2013 at 5:18 | comment | added | Arturo Magidin | Am I the only one who is bugged by questions that start in the title instead of being self-contained in the body? | |
| Apr 27, 2013 at 0:24 | comment | added | Goldstern | Sorry, I misread the question as "Can one characterize amenable groups BY the following property" (which would be silly). | |
| Apr 26, 2013 at 23:39 | comment | added | Misha | @solovei: Now, this, is a reasonable question. For elementary amenable groups, the answer, I think, affirmative (i.e., all such groups are solvable). For nonelementary amenable groups, a comprehensive answer is well beyond the reach of the present technology. However, for the specific question about solvability, I would bet on a counterexample. For instance, I see nothing to prevent existence of a f.g. amenable group with trivial center, where every proper subgroup is cyclic (a version of Tarski monster). (If you ask A.Ol'shansky, he might be able to construct one for you.) | |
| Apr 26, 2013 at 23:22 | comment | added | Misha | @Goldstern: Nonabelian free groups are not amenable. | |
| Apr 26, 2013 at 22:47 | history | edited | Stefan Kohl♦ |
Proper tag.
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| Apr 26, 2013 at 22:26 | comment | added | Goldstern | Which elements of the free group have noncyclic centralizers? | |
| Apr 26, 2013 at 22:00 | history | asked | i. m. soloveichik | CC BY-SA 3.0 |