Vol. 48, No. 2, 1973

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ISSN: 0030-8730
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