Bilinear flocks of quadratic cones

被引：0

作者：

Biliotti M. ^{[1
]}

Johnson N.L. ^{[2
]}

机构：

[1] Dipartimento di Matematica, Université di Lecce, 73100 Lecce, Via Arnesano

[2] Department of Mathematics, University of Iowa, Iowa City, IA

来源：

Journal of Geometry | 1999年 / 64卷 / 1-2期

关键词：

Translation Plane; Collineation Group; Quadratic Cone; Infinite Field;

D O I：

10.1007/BF01229210

中图分类号：

学科分类号：

摘要：

A construction is given which provides infinitely many examples of bilinear flocks of quadratic cones in PG(3,K) where K is an infinite field. The corresponding translation planes admit SL(2, K) as a collineation group. © Birkhäuser Verlag, Basel, 1999.

引用

页码：16 / 50

页数：34

共 27 条

[1]

Bader L., Lunardon G., Thas J.A., Derivation of flocks of quadratic cones, Forum Mathematicum, 2, pp. 163-174, (1990)

[2]

Betten D., On the classification of 4-dimensional flexible projective planes. Mostly Finite Geometries, Lecture Notes in Pure and Applied Mathematics, 190, pp. 9-34, (1997)

[3]

De Clerck F., Van Maldeghem H., Flocks of an infinite quadratic cone, Bull. Belgian Math. Soc./Simon Stevin, 2, 3, pp. 399-415, (1994)

[4]

Dembowski P., Finite Geometries, (1967)

[5]

Dleudonne J., La Géométrie des Groupes Classiques, (1955)

[6]

Foulser D.A., Johnson N.L., The translation planes of order q2 that admit SL(2,q) as a collineation group. I. even order, J. Algebra, 86, pp. 385-406, (1984)

[7]

The translation planes of order q2 that admit SL(2, q) as a collineation group. II. Odd order, J. Geom., 18, pp. 122-139, (1982)

[8]

Foulser D.A., Johnson N.L., Ostrom T.G., Characterization of the Desarguesian planes of order q2 by SL(2, q), Internat. J. Math., and Math. Sci., 6, pp. 605-608, (1983)

[9]

Gevaert H., Johnson N.L., On maximal partial spreads in PG(3,q) of cardinalities q2 - G + 1, q2 - q + 2, Ars Combin., 26, pp. 191-196, (1988)

[10]

Gevaert H., Johnson N.L., Flocks of quadratic cones, generalized quadrangles, and translation planes, Geom. Dedicata, 27, pp. 301-317, (1988)

← 1 2 3 →