Timeline for Finitely generated solvable groups all of whose abelian normal subgroups are finite
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2013 at 10:45 | vote | accept | Alireza Abdollahi | ||
| Nov 2, 2013 at 10:39 | answer | added | YCor | timeline score: 7 | |
| Nov 2, 2013 at 9:44 | history | edited | Alireza Abdollahi | CC BY-SA 3.0 |
added 123 characters in body
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| Nov 1, 2013 at 20:29 | comment | added | YCor | PS: my first comment implies however that every infinite residually finite solvable group has an infinite abelian normal subgroup. | |
| Nov 1, 2013 at 20:23 | comment | added | YCor | However, the classical example of a group with finite derived subgroup but center of infinite index (see Derek's post in MathSE: math.stackexchange.com/questions/272152/…) is probably a source of infinite f.g. solvable groups with no infinite abelian normal subgroups, by taking the semidirect product of Derek's example with $\mathbf{Z}$ shifting the $x_i,y_i$. | |
| Nov 1, 2013 at 20:20 | comment | added | YCor | The naive way to try to prove that these are only finite solvable groups results in: every infinite solvable group has an infinite step-2 nilpotent normal subgroup whose derived subgroup is finite. | |
| Nov 1, 2013 at 19:59 | comment | added | Stefan Kohl♦ | I think a classification and a presentation are two different things -- maybe you can clarify what kind of classification you are looking for? -- Up to isomorphism (seems asking a lot here), or what else? | |
| Nov 1, 2013 at 19:38 | history | asked | Alireza Abdollahi | CC BY-SA 3.0 |