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  1. Path: sparky!uunet!olivea!decwrl!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
  2. From: werner@pell.anu.edu.au (Werner Nickel)
  3. Newsgroups: sci.math.research
  4. Subject: Re: presentation of 2.HJ
  5. Message-ID: <WERNER.92Jul23012900@carslaw.anu.edu.au>
  6. Date: 23 Jul 92 06:29:00 GMT
  7. References: <ARA.92Jul19044622@camelot.ai.mit.edu>
  8. Sender: Daniel Grayson <dan@math.uiuc.edu>
  9. Organization: Australian National University
  10. Lines: 18
  11. Approved: Daniel Grayson <dan@math.uiuc.edu>
  12. X-Submissions-To: sci-math-research@uiuc.edu
  13. X-Administrivia-To: sci-math-research-request@uiuc.edu
  14. In-Reply-To: ara@zurich.ai.mit.edu's message of 19 Jul 92 09:46:22 GMT
  15.  
  16.  
  17. The following is a presentation for the double cover 2.HJ of HJ:
  18.  
  19.            < a, b, c, d, e | c = ab, d = ab^(-1)e, a^2 = e,
  20.                          b^3 = e, c^15,
  21.                      (c^4d^2c^3d^3)^2 = e,
  22.                          (c^3d(c^2d^2)^2)^2 = e,
  23.                          [a,e], [b,e], [c,e], [d,e], e^2 >
  24.  
  25. Comparing this presentation with the ATLAS presentation for HJ shows
  26. that HJ.2/<e> = HJ. By computing the largest abelian quotient one
  27. shows that the group above is perfect. Therefore the group given by
  28. the presentation above is the double cover of HJ.2.
  29.  
  30. Werner Nickel
  31. Mathematics Research Section
  32. Australian National University
  33. Canberra
  34.