Central automorphisms of Veblenian nearaffine planes

• Autorzy: Cudna-Lasecka K. , Jakóbowski J.

Identyfikatory

DOI

10.4064/ba53-3-11

• Języki publikacji: EN

Abstrakty

EN

The paper deals with nearaffine planes described by H. A. Wilbrink. We consider their central automorphisms, i.e. automorphisms satisfying the Veblen condition, which become central collineations in connected projective planes. Moreover, a concept of central pseudo-automorphism is considered, i.e. some bijections in a nearaffine plane are not automorphisms but they become central collineations in the related projective planes.

Słowa kluczowe

EN

affine plane; central automorphism; collineation; Desargues postulate; nearaffine plane; projective plane; Veblen condition

PL

przekształcenie afiniczne; płaszczyzna rzutowa; warunek Veblena

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2005
• Tom: Vol. 53, no 3
• Strony: 337--347
• Opis fizyczny: Bibliogr. 5 poz., wykr.

Twórcy

autor

Cudna-Lasecka K.

• Faculty of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, Żołnierska 14, 10-561 Olsztyn, Poland

autor

Jakóbowski J.

• Faculty of Mathematics and Informatics, University of Warmia and Mazury in Olsztyn, Żołnierska 14, 10-561 Olsztyn, Poland

Bibliografia

• [1] J. André, On finite non-commutative affine spaces, in M. Hall and J. H. von Lint (eds.), Combinatorics, Part I, Math. Centre Tracts 55, 1974, 60-107.
• [2] P. Dembowski, Finite Geometries, Springer, Berlin, 1968.
• [3] J. Jakóbowski, Nearaffine planes related to pseudo-ordered fields, Bull. Polish Acad. Sci. Math. 50 (2002), 345-360.
• [4] G. Pickert, Projektive Ebenen, Springer, Berlin, 1955.
• [5] H. A. Wilbrink, Nearaffine planes, Geom. Dedicata 12 (1982), 53-62.