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On the second cohomology of GL (n, 2)

Published online by Cambridge University Press:  09 April 2009

U. Dempwolff
U. Dempwolff
Affiliation:
Ohio State University Department of Mathematics Columbus, Ohio 43210, U.S.A.
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The purpose of this note is to prove the following result. Theorem A. Let G be a finite group with the following properties (i) V▵ G, &V& = 2n and V is elementary abelian, (ii) G/V ≃ GL(n, 2), (iii) CG(V) ⊆ V. If n ≧ 6 then G splits over V.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 2 , September 1973 , pp. 207 - 209
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Ulrich, Dempwolff, ‘Zentralisation zentraler Involutionen in Ln (2)’ (submitted for publication Ill. J. Math.).Google Scholar
[2]Robert, L. Griess Jr, ‘Schur multipliers of the known finite simple groups’, Bull. Amer. Math. Soc. 78 (1972), 68–71.Google Scholar
[3]Robert, L. Gtiess Jr, ‘Automorphisms of extraspecial groups and nonvanishing degree 2 cohomology’, (to appear).Google Scholar
[4]Bertram, Huppert.Endliche Gruppern I (Springer, Berlin, 1967).Google Scholar
[5]Harriet, Pollatsek, ‘First cohomology groups of some linear groups over fields of characteristic two’. III. J. Math. 15 (1971), 393–417.Google Scholar