Timeline for Any way around Abel's impossibility theorem?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 13, 2019 at 8:26 | comment | added | Daniele Tampieri | Perhaps this Q&A on the Math.SE could give some insight on what happens when the degree $n$ is $>4$. | |
| Dec 13, 2019 at 5:00 | comment | added | Gerry Myerson | Quintics are solvable if you allow solutions of $x^5+x+a$ (but that's in addition to radicals, not in place of them). | |
| Dec 13, 2019 at 3:28 | comment | added | MCH | Yes, you can use any root of any equation p_i = alpha for any i and alpha. | |
| Dec 13, 2019 at 3:10 | comment | added | LSpice | What does "A 'generalized radical' is a solution to $p_i = \alpha$" mean? Does it mean that we are allowed to insert a symbol $\sigma_{i, \alpha}$ anywhere in an equation, and the equation is judged to be correct if some choice, for each such symbol, of a solution $\sigma$ of $p_i(\sigma) = \alpha$ makes it so? (I mean to say, is a generalised radical a specific element of the field, or a place-holder that can stand for any one of potentially many such elements?) | |
| Dec 13, 2019 at 3:03 | comment | added | David E Speyer | There is a paper of Abhyankar which I believe shows that the answer is "no". See my answer at mathoverflow.net/a/61558/297 . | |
| Dec 13, 2019 at 2:56 | history | edited | MCH | CC BY-SA 4.0 |
added 167 characters in body
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| Dec 13, 2019 at 2:50 | history | asked | MCH | CC BY-SA 4.0 |