Talk:Abel–Ruffini theorem

message: The similarities between the proof in this article and the one on Everything2 are most likely unmissable, but that should surprise no one, as I wrote both of them, and they're based on the exposition given in Fraleigh's Abstract Algebra book. Stormwyrm (talk) 10:30, 9 October 2008 (UTC)
thread_title:  Non-Plagiarism from E2 

message: I am not going to attempt to edit the article because I do not understand it, but I would like to raise a question about a step in the argument that appears to be incorrect or is at least unclear (to me).
In the section "Proof" it is stated that "the automorphisms \sigma' also leave E fixed."  As I understand it, the earlier statement that "every permutation \sigma ... induces an automorphism \sigma' on E that leaves Q fixed" means that \sigma' leaves Q point-wise fixed. This seems right.  But as for \sigma' leaving E fixed, it is either trivially true that \sigma' leaves E non-point-wise fixed (that is, \sigma' maps E into itself), as \sigma' is an automorphism, or it is false that \sigma' leaves E point-wise fixed, because, for example, it might swap y_1 with y_2.  (It is true that some induced \sigma acting on E[x] leaves certain elements of E[x], such as f(x), fixed.)
So that's my point of confusion.  I hope this feedback is helpful.
71.183.88.158 (talk) 14:43, 2 March 2012 (UTC)
thread_title:  Statement that "the automorphisms <math>\sigma'</math> also leave <math>E</math> fixed" seems incorrect 

message: The proof seems to show that Q adjoin five transcendentals has degree 25 over Q, which is absurd. The base field in the argument needs to be changed to the transcendental extension of Q generated by the elementary symmetric functions (i.e. the field the coefficients of f lies in).  — Preceding unsigned comment added by 68.40.207.129 (talk) 03:24, 30 July 2012 (UTC)
thread_title: The proof is broken

message: This article uses Galois' approach to prove the theorem which was first proved by Abel.  Why not include Abel's original proof, or at least a description of it?  I have never seen Abel's proof and I am curious about it and would like to see it if it is not terribly complicated.  If it is similar to that of Galois, then perhaps a description of the differences would suffice.  For that matter, I would like to know about Ruffini's incomplete proof as well.  — Anita5192 (talk) 05:38, 13 October 2013 (UTC)
replies: text: See Pesic's book (which I've just added to bibliography). It contains a translation of Abel's paper, among other things. 5.12.29.230 (talk) 09:36, 12 March 2015 (UTC)
replies: text:  Thank you!  I will look it up. — Anita5192 (talk) 03:01, 13 March 2015 (UTC)
thread_title:  Abel's proof 

message: I think there is something inaccurate (or even inexact) in the section "Interpretation". 
The sentence :
"The theorem says that not all solutions of higher-degree equations can be obtained by starting with the equation's coefficients and rational constants, and repeatedly forming sums, differences, products, quotients, and radicals (n-th roots, for some integer n) of previously obtained numbers." 
It is clear from the context that this sentence is relative to equations with numerical coefficients, not to those with litteral coefficients. But Abel's theorem does not say this. It only says that there is no general formula to solve the general equation of degree n (with litteral coefficients). 
Suppose that for each polynomial P with numerical coefficients, there would exist a particular solution by radicals (of different form for each polynomial). It is not at all obvious, if possible, to prove that this would imply the existence of a general formula (this would if it is supposed that the form of the solution is the same for an infinite number of polynomials). Whence my question. Michael Bensimhoun (talk) 08:38, 9 July 2014 (UTC)
thread_title: Inaccuracy

message: Viewing this article with Chrome 87.0.4280.88, the minus signs in the superscripted and subscripted expression "5-n" do not render in the expression for the coefficients of x^n in P(x) difficult to interpret. (This follow the expansion of P(x).) I happened to open the same page in Firefox, and suddenly it made sense.  I have no idea whether there's an alternate way to write it that would render properly.Captain Puget (talk) 16:57, 20 December 2020 (UTC)
replies: text: This is happening in several articles.  I just put in a help request at Wikipedia:Village pump (proposals)#Minus signs not rendering.—Anita5192 (talk) 17:17, 20 December 2020 (UTC)
thread_title:  Poor rendering with Chrome is confusing 

message: I think "wich a cyclic quotient group." is wrong, should it be "with a cyclic quotient group."? ϢereSpielChequers 13:13, 23 June 2021 (UTC)
replies: text: Typo fixed, with a minor clarification. D.Lazard (talk) 15:05, 23 June 2021 (UTC)
thread_title: Wich?

message: "On the other hand, for n ≤ 4, the symmetric group and all its subgroups are solvable. Somehow, this explains the existence of the quadratic, cubic, and quartic formulas."
How do we know that explains the existence of them, if we don't know how? How do we know that without proving it? Isn't that the whole point of mathematics? Anonymous7002 (talk) 04:58, 20 May 2022 (UTC)
replies: text: I have completed the sentence for clarification. D.Lazard (talk) 08:31, 20 May 2022 (UTC)
thread_title:  Somehow