On collineation groups of finite planes
نویسنده
چکیده
From the Introduction to P. Dembowski’s Finite Geometries, Springer, Berlin 1968: “ . . . An alternative approach to the study of projective planes began with a paper by BAER 1942 in which the close relationship between Desargues’ theorem and the existence of central collineations was pointed out. Baer’s notion of (p, L)–transitivity, corresponding to this relationship, proved to be extremely fruitful. On the one hand, it provided a better understanding of coordinate structures (here SCHWAN 1919 was a forerunner); on the other hand it led eventually to the only coordinate–free, and hence geometrically satisfactory, classification of projective planes existing today, namely that by LENZ 1954 and BARLOTTI 1957. Due to deep discoveries in finite group theory the analysis of this classification has been particularly penetrating for
منابع مشابه
The Collineation Groups of Division Ring Planes. I. Jordan Algebras by Robert H. Oehmke and Reuben Sandler
In this note, we outline a method which reduces the determination of the collineation group of a division ring plane to the solution of certain algebraic problems—in particular, to the question of when two rings of a certain type are isomorphic. This method is then applied to planes coordinatized by finite dimensional Jordan algebras of characteristic 5^2, 3, and their collineation groups are d...
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