Vol. 63, No. 2, 1976

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The splitting of extensions of SL(3,3) by the vector space F33.

Robert L. Griess, Jr.

Vol. 63 (1976), No. 2, 405–409
Abstract

We give two proofs that H2(SL(3,3),F33) = 0. This result has appeared in a paper by Sah, [6], but our methods are relatively elementary, i.e., we require only elementary homological algebra and do a group-theoretic analysis of an extension of SL (3, 3) by F33 to show that the extension splits. The starting point is to notice that the vector space is a free module for F3(x), where x has Jordan canonical form ( 1 1  0)
( 0 1  1)
0 0  1 . We then can exploit the vanishing of Hi(x,F33) i = 1,2.

Mathematical Subject Classification 2000
Primary: 18H10, 18H10
Secondary: 20D05
Milestones
Received: 31 October 1974
Published: 1 April 1976
Authors
Robert L. Griess, Jr.
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor MI 48109-1043
United States