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- W2014080606 abstract "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 3 4 ) (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 Q and 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)." @default.
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- W2014080606 date "1969-01-01" @default.
- W2014080606 modified "2023-10-04" @default.
- W2014080606 title "Collineation Groups of Generalized André Planes" @default.
- W2014080606 doi "https://doi.org/10.4153/cjm-1969-036-7" @default.
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