Vol. 48, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
Automorphisms of extra special groups and nonvanishing degree 2 cohomology

Robert L. Griess, Jr.

Vol. 48 (1973), No. 2, 403–422

If E is an extra-specia12-group, it is known that Aut (E)Inn (E) is isomorphic to an orthogonal group. We prove that this extension is nonsplit, except in small cases. As a consequence, the nonvanishing of the second cohomology groups of certain classical groups (defined over F2) on their standard modules may be inferred. Also, a criterion for a subgroup of these orthogonal groups to have a nonsplit extension over the standard module is given.

Mathematical Subject Classification 2000
Primary: 20J05
Secondary: 10C30
Received: 25 May 1972
Revised: 8 March 1973
Published: 1 October 1973
Robert L. Griess, Jr.
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor MI 48109-1043
United States