Local Recognition Of Non-Incident Point-Hyperplane Graphs |
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| Authors: | Arjeh M Cohen Hans Cuypers Ralf Gramlich |
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| Institution: | (1) Department of Mathematics and Computer Science, Technische University Eindhoven, 513, 5600 MB Eindhoven, The Netherlands;(2) Department of Mathematics and Computer Science, Technische University Eindhoven, 513, 5600 MB Eindhoven, The Netherlands;(3) TU Darmstadt FB Mathematik AG 5, Schloßgartenstraße 7, 64289 Darmstadt, Germany |
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| Abstract: | Let  be a projective space. By H() we denote the graph whose vertices are the non-incident point-hyperplane pairs of , two vertices (p,H) and (q,I) being adjacent if and only if p  I and q H. In this paper we give a characterization of the graph H() (as well as of some related graphs) by its local structure. We apply this result by two characterizations of groups G with PSL
n
(
) GPGL
n
(
), by properties of centralizers of some (generalized) reflections. Here
is the (skew) field of coordinates of . |
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| Keywords: | 05C25 20D06 20E42 51E25 |
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