Geodesic
Collineation Groups of Generalized André Planes
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 358-369

Voir la notice de l'article provenant de la source Cambridge University Press

In a previous paper (5), I constructed a class of translation planes, called generalized André planes or λ-planes, and discussed the associated autotopism collineation groups. The main question unanswered in (5) is whether or not there exists a collineation η of a λ-plane Π which moves the two axes of Π but does not interchange them.The answer to this question is “no”, except if Π is a Hall plane (or possibly if the order n of Π is 34) (Corollary 2.8). This result makes it possible to determine the isomorphisms between λ-planes. More specifically, let Π and Π′ be two λ-planes of order n coordinatized by λ-systems Qand Q′, respectively. Then, except possibly if n = 34, Π and Π′ are isomorphic if and only if Q and Q′ are isotopic or anti-isotopic (Corollary 2.13). In particular, Π is an André plane if and only if Q is an André system (Corollary 2.14). 
Foulser, David A. Collineation Groups of Generalized André Planes. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 358-369. doi: 10.4153/CJM-1969-036-7
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