Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Presentations for 3-Dimensional Special Linear Groups Over Integer Rings

Marston Conder, Edmund Robertson and Peter Williams
Proceedings of the American Mathematical Society
Vol. 115, No. 1 (May, 1992), pp. 19-26
DOI: 10.2307/2159559
Stable URL: http://www.jstor.org/stable/2159559
Page Count: 8
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Presentations for 3-Dimensional Special Linear Groups Over Integer Rings
Preview not available

Abstract

The following 2-generator 6-relator presentation is obtained for the 3-dimensional special linear group SL(3, Zk) for each odd integer $k > 1:$ \begin{equation*}\begin{split} \mathrm{SL}(3, \mathbb{Z}_k) = \langle x, y\mid x^3 = y^3 = (xy)^6 = (x^{-1}yx^{-1}y^{-1}xy)^2 \\ = (xy^{-1}xyxy^{-1}x^{-1}y^{-1})^k \\ =((xy^{-1}xyxy^{-1}x^{-1}y^{-1})^{(k - 1)/2}xy)^4 = 1\rangle.\end{split} \end{equation*} Alternative presentations for these groups and other groups associated with them are also given.

Page Thumbnails

  • Thumbnail: Page 
19
    19
  • Thumbnail: Page 
20
    20
  • Thumbnail: Page 
21
    21
  • Thumbnail: Page 
22
    22
  • Thumbnail: Page 
23
    23
  • Thumbnail: Page 
24
    24
  • Thumbnail: Page 
25
    25
  • Thumbnail: Page 
26
    26