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.

The Alternating Group a₈ and the General linear Group GL₄(2)

John Murray
Mathematical Proceedings of the Royal Irish Academy
Vol. 99A, No. 2 (Dec., 1999), pp. 123-132
Published by: Royal Irish Academy
Stable URL: http://www.jstor.org/stable/20459753
Page Count: 10
  • Read Online (Free)
  • Download ($10.00)
  • 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.
The Alternating Group a₈ and the General linear Group GL₄(2)
Preview not available

Abstract

We give an explicit construction for the isomorphism A₈ ≅ GL₄(2). The involutions of cycle type 2³ in the symmetric group S₆, together with the null-set, can be given the structure of an elementary abelian group of order 16, in such a way that S₆ preserves the group operation. This gives an embedding ζ of S₆ into the general linear group GL₄(2). Regarding S₆ as a subgroup of the alternating group A₈, we show that ζ extends to A₈. Coincidence of group orders implies that this extension is an isomorphism.isomorphism.

Page Thumbnails

  • Thumbnail: Page 
[123]
    [123]
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131
  • Thumbnail: Page 
132
    132