On a Baer involution which maps an oval into itself

Olga Fernandes

doi:10.1007/bf01229331

On a Baer involution which maps an oval into itself

Archiv der Mathematik ◽

10.1007/bf01229331 ◽

1985 ◽

Vol 44 (5) ◽

pp. 467-471

Author(s):

Olga Fernandes

Keyword(s):

Baer Involution

On Baer Involutions of Finite Projective Planes

Canadian Journal of Mathematics ◽

10.4153/cjm-1970-100-6 ◽

1970 ◽

Vol 22 (4) ◽

pp. 878-880 ◽

Cited By ~ 1

Author(s):

Judita Cofman

Keyword(s):

Projective Plane ◽

Finite Projective Plane ◽

Projective Planes ◽

Desarguesian Projective Plane ◽

Finite Projective Planes ◽

Special Cases ◽

Collineation Groups ◽

Baer Involution ◽

Finite Desarguesian Projective Plane

1. An involution of a projective plane π is a collineation X of π such that λ2 = 1. Involutions play an important röle in the theory of finite projective planes. According to Baer [2], an involution λ of a finite projective plane of order n is either a perspectivity, or it fixes a subplane of π of order in the last case, λ is called a Baer involution.While there are many facts known about collineation groups of finite projective planes containing perspectivities (see for instance [4; 5]), the investigation of Baer involutions seems rather difficult. The few results obtained about planes admitting Baer involutions are restricted only to special cases. Our aim in the present paper is to investigate finite projective planes admitting a large number of Baer involutions. It is known (see for instance [3, p. 401]) that in a finite Desarguesian projective plane of square order, the vertices of every quadrangle are fixed by exactly one Baer involution.