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Translation generalized quadrangles
Authors: --- ---
ISBN: 1281924512 9786611924515 981277291X 9789812772916 9812569510 9789812569516 Year: 2006 Volume: v. 26 Publisher: Singapore London World Scientific

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Abstract

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

An algebraic structure for Moufang quadrangles
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ISBN: 0821836080 Year: 2005 Publisher: Providence, R.I. American Mathematical Society

Q-clan geometries in characteristic 2
Authors: ---
ISBN: 9783764385071 3764385073 9786611179731 1281179736 3764385081 Year: 2007 Publisher: Basel : Birkhäuser,

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Abstract

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. .

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