Timeline for Is there a precise notion of "almost all" such that almost all finite groups are Galois groups of extensions of the rationals?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 3, 2014 at 14:04 | history | edited | Lee Mosher |
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| Apr 29, 2014 at 20:28 | vote | accept | Sylvain JULIEN | ||
| Apr 29, 2014 at 18:15 | answer | added | Nick Gill | timeline score: 17 | |
| Apr 29, 2014 at 15:33 | comment | added | Nick Gill | Derek Holt makes some interesting comments about conjectured properties of "almost all finite groups", in his answer to this question: mathoverflow.net/questions/164202/… you might find it of interest... | |
| Apr 29, 2014 at 3:34 | comment | added | Colin Reid | Proving almost all finite groups are 2-groups looks hard, but perhaps it is reasonable to assert that almost all finite groups are soluble, since non-abelian simple groups are extremely sparse in the class of finite groups and don't admit many extensions. | |
| Apr 28, 2014 at 21:16 | review | Close votes | |||
| Apr 29, 2014 at 11:01 | |||||
| Apr 28, 2014 at 20:04 | comment | added | Joël | Alex, you're right, I checked on wikipedia and it is said to be "a folklore conjecture". So my comment is wrong. I leave it as it may help precise the question: it proposes a natural notion of "almost all finite groups" for which the Galois-theoretic question "are almost all finite groups galois groups over $\mathbb Q$?" can be reduced to a Group-theoretic conjecture. Is it possible to prove with current technology that almost all finite groups are Galois groups over $\mathbb Q$ in that sense ? | |
| Apr 28, 2014 at 19:56 | comment | added | Alex Becker | @Joël Is "almost all finite groups are $2$-groups" actually known? I was under the impression it was still open. | |
| Apr 28, 2014 at 19:45 | comment | added | Joël | Since "almost all finite groups are 2-groups" in the sense that the proportion of isom. classes of groups of order up to $x$ that are $2$-groups goes to $1$ when $x$ goes to infinity, and since all $2$-groups are nilpotent, hence solvable, and since all solvable have been shown by Shafarevich to be Galois groups of finite extensions over $\mathbb Q$, then the answer to your question is yes. | |
| Apr 28, 2014 at 19:24 | history | asked | Sylvain JULIEN | CC BY-SA 3.0 |