Timeline for Solvable transitive groups of prime degree
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Mar 19, 2011 at 12:17 | history | edited | Chandan Singh Dalawat | CC BY-SA 2.5 |
cosmetics; added 21 characters in body
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| Mar 19, 2011 at 10:36 | history | edited | Chandan Singh Dalawat | CC BY-SA 2.5 |
improved title
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| Mar 19, 2011 at 6:40 | answer | added | Chandan Singh Dalawat | timeline score: 4 | |
| Jun 12, 2010 at 5:57 | comment | added | Chandan Singh Dalawat | Pour qu'une équation de degré premier soit résoluble par radicaux, il faut et il suffit que deux quelconques de ces racines étant connues, les autres s'en déduisent rationnellement (Évariste Galois, Bulletin de M. Férussac, XIII (avril 1830), p. 271). | |
| May 13, 2010 at 14:38 | comment | added | Emerton | I should add: Kronecker did publish a proof of that result; I just don't understand why it wasn't already seen at the time to be a consequence of Galois's more general result. | |
| May 13, 2010 at 14:36 | comment | added | Emerton | Yes, that is a very nice corollary. For a reason I don't understand (because of the chronology: Galois is well before Kronecker), that result is traditionally attributed to Kronecker. A highly recommened reference for the history of these ideas is Hans Wussing's "The genesis of the abstract group concept". | |
| May 13, 2010 at 9:22 | comment | added | Chandan Singh Dalawat | Amazing! Great scholarship! I had guessed that such a result should be true from a reference to Artin's Galois Theory (Notre Dame notes), Chapter 3, Theorem 7, written by AN Milgram. He gives another nice corollary: a solvable irreducible prime-degree polymonial over a subfield of the reals has either (precisely) one real root or all its roots are real. | |
| May 13, 2010 at 5:42 | comment | added | Emerton | A remark: this result is due to Galois himself, I believe. As an application: note that any subgroup of $AGL(1,p)$ that fixes two elements is trivial, and conversely, any transitive subgroup of $S_p$ with this property is contained in $AGL(1,p)$. Thus we get Galois's theorem: a prime degree irred. polynomial is solvable if and only if its splitting field is generated by any two roots. (This result was regarded as Galois's major contribution to the theory of equations for a decade or two after his death.) | |
| May 13, 2010 at 1:57 | history | edited | Chandan Singh Dalawat | CC BY-SA 2.5 |
Addendum
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| May 11, 2010 at 4:34 | vote | accept | Chandan Singh Dalawat | ||
| May 10, 2010 at 12:33 | answer | added | Robin Chapman | timeline score: 13 | |
| May 10, 2010 at 12:04 | answer | added | Jack Schmidt | timeline score: 12 | |
| May 10, 2010 at 11:26 | history | asked | Chandan Singh Dalawat | CC BY-SA 2.5 |