Timeline for Is this system always solvable in radicals by quartics, octics, $12$-ics, etc?
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| Dec 26, 2022 at 13:22 | vote | accept | Tito Piezas III | ||
| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Jan 6, 2016 at 23:00 | answer | added | Peter Mueller | timeline score: 6 | |
| Jan 6, 2016 at 19:51 | comment | added | eric | (the point being that by standard Hilbert irreducibility methods coming from arithmetic, if you can compute the geometric Galois group then you'll in general be able to find rational values of $\alpha$ etc such that eveything specialises but the Galois group doesn't get any smaller). What I'm saying is that this question is tagged number theory but is actually a question in complex algebraic geometry. | |
| Jan 6, 2016 at 19:47 | comment | added | eric | The equations are symmetric in the $x_i$ of course, so they are actually 4 equations in the four unknowns given by the first four elementary symmetric polynomials in the $x_i$. This divides the degree of everything by 24 and puts an $S_4$ on the top (which is solvable) which makes me worry that what you have seen computationally is a low-dimensional coincidence. I think also that this is a question about geometry rather than arithmetic; probably this is a question about the extension $C(x_1,x_2,x_3,x_4)/C(\alpha,\beta,\gamma,\delta)$ with $\alpha$ etc independent transcendental vars. | |
| Jan 6, 2016 at 18:52 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Removed phrase.
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| Jan 6, 2016 at 18:28 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
added 73 characters in body
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| Jan 6, 2016 at 18:21 | history | asked | Tito Piezas III | CC BY-SA 3.0 |