On the Non-Existence of Certain Cameron-Liebler Line Classes in PG(3, q)

被引：5

作者：

Bruen A.A. ^{[1
]}

Drudge K. ^{[1
]}

机构：

[1] Department of Mathematics, University of Western Ontario, London

来源：

Designs, Codes and Cryptography | 1998年 / 14卷 / 2期

关键词：

Finite fields; Finite linear groups; Finite projective spaces; Incidence matrices; Spreads;

D O I：

10.1023/A:1008231927955

中图分类号：

学科分类号：

摘要：

Our main result is a non-existence theorem for certain families of lines in three dimensional projective space PG(3, q) over a finite field GF(q). Specifically, a Cameron-Liebler line class in PG(3, q) is a set of lines which intersects every spread of PG(3, q) in the same number x of lines (this number is called its parameter). These sets arose in connection with an attempt by Cameron and Liebler to determine the subgroups of PGL(n+1, q) which have the same number of orbits on points (of PG(n, q))as on lines; they satisfy several equivalent properties. Here we prove that for 2 < x ≤ √q, no Cameron-Liebler line class of parameter x exists in PG(3, q). A relevant general question on incidence matrices is described.

引用

页码：127 / 132

页数：5

共 5 条

[1] Bruen, A.A., Double Fives and Double Sixes, , manuscript
[2] Cameron, P.J., Liebler, R.A., Tactical decompositions and orbits of projective groups (1982) Lin. Alg. Appl., 46, pp. 91-102
[3] Dembowski, P., (1968) Finite Geometries, , Springer-Verlag, Berlin-Heidelberg, New York
[4] Eisfeld, J., On the Common Nature of Spreads and Pencils in PG(d, q) Discrete Mathematics, , submitted
[5] Penttila, T., Cameron-Liebler line classes in PG(3, q) (1991) Geom. Ded., 37, pp. 245-252

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