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A Course on Elation Quadrangles

Thas, Koen,

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A Course on Elation Quadrangles

Record Type:	Electronic resources : Monograph/item
Title/Author:	A Course on Elation Quadrangles/ Koen Thas
Author:	Thas, Koen,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2012,
Description:	1 online resource (129 pages)
Subject:	Combinatorics & graph theory -
Online resource:	https://doi.org/10.4171/110
Online resource:	https://www.ems-ph.org/img/books/thas_mini.jpg
ISBN:	9783037196106

A Course on Elation Quadrangles
Thas, Koen,

A Course on Elation Quadrangles[electronic resource] /Koen Thas - Zuerich, Switzerland :European Mathematical Society Publishing House,2012 - 1 online resource (129 pages) - EMS Series of Lectures in Mathematics (ELM) ;2523-5176.

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

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.

ISBN: 9783037196106

Standard No.: 10.4171/110doiSubjects--Topical Terms:

3480941
Combinatorics & graph theory

A Course on Elation Quadrangles
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520 $a 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.
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