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Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global "Moufang Condition", a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated. Translation Generalized Qu
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Geometry --- Finite generalized quadrangles. --- Finite geometries. --- Rings (Algebra) --- Finite generalized quadrangles --- Finite geometries --- Algebraic rings --- Ring theory --- Algebraic fields --- Geometries, Finite --- Combinatorial geometry --- Generalized quadrangles, Finite --- Quadrangles, Generalized finite
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This monograph offers the only comprehensive, coherent treatment of the theory - in characteristic 2 - of the so-called flock quadrangles, i.e., those generalized quadrangles (GQ) that arise from q-clans, along with their associated ovals. Special attention is given to the determination of the complete oval stabilizers of each of the ovals associated with a flock GQ. A concise but logically complete introduction to the basic ideas is given. The theory of these flock GQ has evolved over the past two decades and has reached a level of maturation that makes it possible for the first time to give a satisfactory, unified treatment of all the known examples. The book will be a useful resource for all researchers working in the field of finite geometry, especially those interested in finite generalized quadrangles. It is of particular interest to those studying ovals in finite Desarguesian planes. .
Finite generalized quadrangles. --- Automorphisms. --- Automorphismes --- Finite generalized quadrangles --- Automorphisms --- Algebra --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Generalized quadrangles, Finite --- Quadrangles, Generalized finite --- Mathematics. --- Convex geometry. --- Discrete geometry. --- Convex and Discrete Geometry. --- Combinatorial geometry --- Math --- Science --- Group theory --- Symmetry (Mathematics) --- Finite geometries --- Discrete groups. --- Groups, Discrete --- Infinite groups --- Discrete mathematics --- Convex geometry .
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Ordered algebraic structures --- Buildings (Group theory) --- Global differential geometry --- Finite generalized quadrangles --- Homogeneous spaces. --- Immeubles (Théorie des groupes) --- Géométrie différentielle globale --- Homogeneous spaces --- 512.54 --- 514.7 --- Spaces, Homogeneous --- Lie groups --- Generalized quadrangles, Finite --- Quadrangles, Generalized finite --- Finite geometries --- Geometry, Differential --- Theory of buildings (Group theory) --- Tits's theory of buildings (Group theory) --- Linear algebraic groups --- Groups. Group theory --- Differential geometry. Algebraic and analytic methods in geometry --- 514.7 Differential geometry. Algebraic and analytic methods in geometry --- 512.54 Groups. Group theory --- Immeubles (Théorie des groupes) --- Géométrie différentielle globale --- Global differential geometry. --- Finite generalized quadrangles. --- Immeubles (théorie des groupes) --- Géométrie différentielle globale. --- Quadrangles généralisés. --- Espaces homogènes.
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