Local recognition of non-incident point-hyperplane graphs
Let ℙ be a projective space. By H (ℙ) we denote the graph whose vertices are the non-
incident point-hyperplane pairs of ℙ, 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 (ℙ)(as well as of
some related graphs) by its local structure. We apply this result by two characterizations of
groups G with PSL n (\Bbb F)≤ G≤ PGL n (\Bbb F), by properties of centralizers of some
(generalized) reflections. Here\Bbb F is the (skew) field of coordinates of ℙ.
incident point-hyperplane pairs of ℙ, 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 (ℙ)(as well as of
some related graphs) by its local structure. We apply this result by two characterizations of
groups G with PSL n (\Bbb F)≤ G≤ PGL n (\Bbb F), by properties of centralizers of some
(generalized) reflections. Here\Bbb F is the (skew) field of coordinates of ℙ.
Let ℙ be a projective space. By H(ℙ) we denote the graph whose vertices are the non-incident point-hyperplane pairs of ℙ, 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(ℙ) (as well as of some related graphs) by its local structure. We apply this result by two characterizations of groups G with PSL n ()≤G≤PGL n (), by properties of centralizers of some (generalized) reflections. Here is the (skew) field of coordinates of ℙ.
Springer
Showing the best result for this search. See all results
