A course on elation quadrangles
By: Koen Thas
Series: EMS series of lectures in mathematics; EMS series of lectures in mathematics
Publisher: European Mathematical Society
Published: 2012
Place of publication: Zürich, Switzerland
Language: eng
Number of pages: 116
ISBN-13: 9783037196106; 9783037191101
Copyright date: 2012
Subjects: Finite generalized quadrangles; Mathematical models; Moufang loops; Abelian p-groups; Quadrangles généralisés; Modèles mathématiques; Boucles de Moufang; P-Groupes abéliens; Combinatorics & graph theory; MATHEMATICS / Geometry / General; Combinatorics; Group theory and generalizations; Geometry
Description: The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring for instance a question of Knarr from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor's prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as p-modular cohomology, Heisenberg groups and existence problems for certain translation nets, are briefly touched. The text starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. Containing dozens of exercises at various levels, from very easy to rather difficult, this course will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. The more accomplished mathematician will especially find the final chapters challenging.
Notes: Includes bibliographical references (pages 105-109) and index.