Timeline for On sentences true in all finite groups
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| May 26, 2015 at 4:36 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
put "An interesting alternative..." paragraph at the end and withdrawed "I suspect the answer will be YES for the two questions.""
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| May 25, 2015 at 20:44 | comment | added | Duchamp Gérard H. E. | @EmilJeřábek I think you are right. Then, I modified my text. Thanks. As I did it (too) quickly, I did not explore the fact that any free group can be embedded in a two generator free group. Vote +1 for Bjorn's answer | |
| May 25, 2015 at 20:43 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
Modification of the construction oof the projective limit in order to take the infinite alphabet into account
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| May 24, 2015 at 21:21 | comment | added | Christian Remling | However, for the first sentence, the free group with one generator is enough: If $\forall x\exists y\: w=1$ holds in $\mathbb Z$ and $x\in G$ is given, map $1\mapsto x$ and take as $y$ the image (under this homomorphism) of the $y'\in \mathbb Z$ that exists by assumption. So the (first) sentence holds in all groups precisely if it holds in $\mathbb Z$. | |
| May 24, 2015 at 14:41 | comment | added | Emil Jeřábek | @BjørnKjos-Hanssen: The sentences in question are positive, hence preserved by homomorphic images, and every group is a homomorphic image of a free group. One would need a free group over infinitely many generators for this to work, though. | |
| May 24, 2015 at 9:02 | comment | added | Bjørn Kjos-Hanssen | I don't really see, how do you relate the free group to what's true of all groups? | |
| May 24, 2015 at 6:52 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
positioning
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| May 24, 2015 at 6:43 | history | undeleted | Duchamp Gérard H. E. | ||
| May 24, 2015 at 3:55 | history | deleted | Duchamp Gérard H. E. | via Vote | |
| May 24, 2015 at 3:54 | history | edited | Duchamp Gérard H. E. | CC BY-SA 3.0 |
"Yes" made explicit in the beginning
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| May 24, 2015 at 3:46 | history | answered | Duchamp Gérard H. E. | CC BY-SA 3.0 |