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 analog 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 Quadrangles" is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: "Finite Generalized Quadrangles" (1984) by S E Payne and J A Thas, "Generalized Polygons" (1998) by H Van Maldeghem, and "Symmetry in Finite Generalized Quadrangles" (2004) by K Thas.
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semifield flock, little projective group, translation generalized oval, translation generalized quadrangles, root elation, generalized ovoid, translation ovoid, elation generalized quadrangles, lax embeddings, generalized ovals, elation point, flock generalized quadrangles, linear collineation, elliptic quadric, nontrivial elation, dual affine plane, elation group, given nonsquare, ordinary quadrangle, nonconcurrent lines, distinct collinear points, nonsingular conic, hyperbolic quadric, inversive planes, finite generalized quadrangles Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Veblen, Van Maldeghem, Moufang Condition, Elation Generalized Quadrangles, Moufang Property, Suzuki-Tits Moufang, Tits Condition, Axiom of Ueblen, Johnson's Theorem, Ree-Tits Moufang, Sketch of Proof New!
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semifield flock, little projective group, translation generalized oval, translation generalized quadrangles, root elation, generalized ovoid, translation ovoid, elation generalized quadrangles, lax embeddings, generalized ovals, elation point, flock generalized quadrangles, linear collineation, elliptic quadric, nontrivial elation, dual affine plane, elation group, given nonsquare, ordinary quadrangle, nonconcurrent lines, distinct collinear points, nonsingular conic, hyperbolic quadric, inversive planes, finite generalized quadrangles Key Phrases - Capitalized Phrases (CAPs): (learn more)
Axiom of Veblen, Van Maldeghem, Moufang Condition, Elation Generalized Quadrangles, Moufang Property, Suzuki-Tits Moufang, Tits Condition, Axiom of Ueblen, Johnson's Theorem, Ree-Tits Moufang, Sketch of Proof New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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