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  1. Path: sparky!uunet!ogicse!das-news.harvard.edu!husc-news.harvard.edu!ramanujan!elkies
  2. From: elkies@ramanujan.harvard.edu (Noam Elkies)
  3. Newsgroups: sci.math
  4. Subject: Corrections Re: Abel's proof of the insolubility of the quintic
  5. Message-ID: <1992Sep4.121746.15366@husc3.harvard.edu>
  6. Date: 4 Sep 92 16:17:45 GMT
  7. Article-I.D.: husc3.1992Sep4.121746.15366
  8. References: <1992Sep3.122450.15337@husc3.harvard.edu> <87849@netnews.upenn.edu> <1992Sep4.120349.15365@husc3.harvard.edu>
  9. Organization: Harvard Math Department
  10. Lines: 16
  11. Nntp-Posting-Host: ramanujan.harvard.edu
  12.  
  13. In article <1992Sep4.120349.15365@husc3.harvard.edu> I wrote:
  14. >The identity and simple transpositions together give a union of
  15. >conjugacy classes of size (n^2+n+2)/2,
  16.                               ^^^
  17. of course this should read (n^2-n+2)/2.  (typo)
  18.  
  19. >which divides |A_n|=n!/2 at least for n=11,18,27,37,38,46.
  20.  
  21. These values are correct.  Unfortunately there are no simple
  22. transpositions in A_n.  So let's use 3-cycles instead; then
  23. instead of (n^2-n+2)/2 we have (n^3-3n^2+2n+3)/3.  Here
  24. the first sufficiently smooth value occurs at n=68, when
  25. (n^3-3n^2+2n-3)/3 = 100233 = 3*3*7*37*43.
  26.  
  27. --Noam D. Elkies (elkies@zariski.harvard.edu)
  28.   Dept. of Mathematics, Harvard University
  29.