Covers of Point-Hyperplane Graphs
Arjeh M. Cohen
and E.J. Postma
Technische Universiteit Eindhoven Department of Mathematics and Computer Science Den Dolech 2 Eindhoven The Netherlands Den Dolech 2 Eindhoven The Netherlands
DOI: 10.1007/s10801-005-4530-7
Abstract
A cover of the non-incident point-hyperplane graph of projective dimension 3 for fields of characteristic 2 is constructed. For fields \mathbb F {\mathbb F} of even order larger than 2, this leads to an elementary construction of the non-split extension of SL 4( \mathbb F {\mathbb F} )by \mathbb F {\mathbb F} 6.
Pages: 317–329
Keywords: keywords group extension; graph cover; special linear group; projective geometry
Full Text: PDF
References
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2. N. Biggs, Algebraic Graph Theory, Cambridge, Cambridge University Press, 1974.
3. K.S. Brown, Cohomology of Groups, New York, Springer-Verlag, 1982.
4. R. Gramlich, On Graphs, Geometries, and Groups of Lie Type, Ph.D. thesis, Technische Universiteit Eindhoven, 2002.
5. R.L. Griess, Jr, “Automorphisms of extra special groups and nonvanishing degree 2 cohomology,” Pa- cific J. Math. 48 (1973), 403-422.
6. J. L. Gross and Th. W. Tucker, Topological Graph Theory, New York, John Wiley & Sons, 1987.
7. A. Malni\check c, R. Nedela, and M. \check Skoviera, “Lifting graph automorphisms by voltage assignments,” Europ. J. Combinatorics 21 (2000), 927-947.
8. E. J. Postma, “Covers of graphs related to the general linear group,” M.Sc. thesis, Technische Universiteit Eindhoven, 2003.
9. C.-H. Sah, “Cohomology of split group extensions, II,” J. Algebra 45 (1977), 17-68.