Symmetry in Finite Generalized Quadrangles
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Beschreibung
In this self-contained monograph, finite generalized quadrangles are classified by symmetry, generalizing the celebrated Lenz--Barlotti classification for projective planes. It serves as an introduction to the combinatorial, geometrical, and group-theoretical concepts that arise in the classification and the general theory of finite generalized quadrangles. Several long-standing open problems are solved by using a mixture of geometrical, combinatorial, and group-theoretical arguments. Further, a conjectural classification program for all finite transaltion generalized quadrangles is decribed. The book will be useful to advanced graduate students and researchers in geometry, group theory, or algebraic combinatorics.
Contains many new results, not previously published anywhere else Proof of the main (classification) result is written and split up in such a way that many parts of it can be seen in their own right, and can be used independently Several open problems and longstanding conjectures are completely solved in the book, often by introducing new techniques which can be used in various other situations
Autor*in
Koen Thas
Themen in »Symmetry in Finite Generalized Quadrangles«
Geometrie Lenz-Barlotti-Klassifikation automorphism boundary element method character classification Finite geometry history of mathematics Morphism story symmetry theorem