Thas, Koen 1977
Overview
Works:  14 works in 56 publications in 2 languages and 2,459 library holdings 

Roles:  Author, Editor, Creator 
Publication Timeline
.
Most widely held works by
Koen Thas
Translation generalized quadrangles by
J. A Thas(
)
13 editions published in 2006 in English and held by 1,509 WorldCat member libraries worldwide
1. Generalized quadrangles. 1.1. Finite generalized quadrangles. 1.2. Automorphisms. 1.3. Grids and dual grids. 1.4. The classical generalized quadrangles. 1.5. The generalized quadrangles T[symbol](O) and T[symbol](C) of tits. 1.6. The generalized quadrangles T[symbol](O). 1.7. Orders of the known generalized quadrangles. 1.8. Generalized quadrangles with small parameters  2. Regularity, antiregularity and 3regularity. 2.1. Regularity. 2.2. Regularity and dual nets. 2.3. Antiregularity. 2.4. Antiregularity and Laguerre planes. 2.5. 3regularity. 2.6. 3regularity and subquadrangles. 2.7. 3regularity, inversive planes, and characterizations  3. Elation and translation generalized quadrangles. 3.1. Some notions from group theory. 3.2. Elation generalized quadrangles. 3.3. Translation generalized quadrangles. 3.4. The kernel of a translation generalized quadrangle. 3.5. T(n,m,q)s and translation generalized quadrangles. 3.6. Regular pseudoovals and regular pseudoovoids. 3.7. Automorphisms of translation generalized quadrangles. 3.8. Important properties of O(n,m,q). 3.9. Pseudoovals. 3.10. Eggs. 3.11. The stabilizer of the basepoint of a translation generalized quadrangle. 3.12. Structure of the automorphism group of a translation quadrangle  4. Generalized quadrangles and flocks. 4.1. Flocks. 4.2. Flocks and translation planes. 4.3. Flocks of ovoids and hyperbolic quadrics. 4.4. Flocks of cones. 4.5. Semifield flocks. Known examples of semifield flocks. 4.6. Generalized quadrangles and flocks. 4.7. Semifield flocks and translation generalized quadrangles. 4.8. Derivation and BLTsets. 4.9. Constructions. 4.10. Property (G) for generalized quadrangles of order (s,s[symbol]). 4.11. Flocks, subquadrangles and ovals. Addendum A: isomorphisms of flock quadrangles and associated geometries. 4.12. The fundamental theorem of qclan geometry, and applications. Addendum B: Basic questions on elation groups. 4.13. The standard conjectures and questions. 4.14. Some results by Payne and K. Thas. 4.15. Elation generalized quadrangles with nonisomorphic elation groups  5. Good eggs. 5.1. Good eggs and good translation generalized quadrangles. 5.2. Good eggs and veronese surfaces. 5.3. Coordinatization and applications  6. Generalized quadrangles, nets and the axiom of Veblen. 6.1. Generalized quadrangles and the axiom of Veblen. 6.2. Translation generalized quadrangles and the axiom of Veblen. 6.3. Property (G) and the axiom of Veblen. 6.4. Flock generalized quadrangles and the axiom of Veblen. 6.5. Subquadrangles and the axiom of Veblen. 6.6. Nets and characterizations of translation generalized quadrangles  7. Ovoids and subquadrangles. 7.1. Ovoids of Q(4,q). 7.2. Subquadrangles and ovoids. 7.3. Translation ovoids and semifield flocks. 7.4. Coordinates of the known nonclassical ovoids of Q(4,q). 7.5. Subquadrangles of T(O), with O good: the even case. 7.6. Subquadrangles of T(O), with O good: the odd case. 7.7. Subquadrangles: remaining cases and some applications. 7.8. Translation generalized quadrangles with one classical subquadrangle. 7.9. Elation generalized quadrangles with a subquadrangle  8. Translation generalized ovals. 8.1. Translation generalized ovoids and translation generalized ovals. 8.2. Note on the definition of translation generalized oval/ovoid. 8.3. Characterizations of the T2 (O) of tits. 8.4. A characterization of translation generalized ovals. 8.5. Classification of 2transitive generalized ovals in even characteristic  9. Moufang sets and translation Moufang sets. 9.1. Definition and general results. 9.2. Finite Moufang sets  10. Configurations of translation points. 10.1. Spansymmetric generalized quadrangles. 10.2. Groups admitting a 4Gonal basis. 10.3. SPGQs and Moufang sets. 10.4. Basic structural Lemmas. 10.5. Classification of SPGQs of order (s,t),1<s[symbol]t<s[symbol]. 10.6. SPGQs of order (s,s[symbol]). 10.7. Generalized quadrangles with a line of translation points. 10.8. On the classification of translation generalized quadrangles  11. Moufang quadrangles with a translation point. 11.1. Notation. 11.2. Some general elementary Lemmas. 11.3. The Moufang property and analogues. 11.4. Tits generalized quadrangles and tits systems. 11.5. Properties of Moufang quadrangles. 11.6. Half 3Moufang quadrangles. 11.7. 2Moufang quadrangles and FongSeitz quadrangles. 11.8. Conclusion  12. Translation ovoids in translation quadrangles. 12.1. Ovoids, elation or translation with respect to a flag or a point. 12.2. Selfpolar elation generalized quadrangles. 12.3. SuzukiTits Moufang sets. 12.4. Subtended elation ovoids  13. Translation generalized quadrangles in projective space. 13.1. Generalities about Lax embeddings. 13.2. Planar translationhomogeneous embeddings. 13.3. Exceptional nonplanar translationhomogeneous embeddings. 13.4. Nonplanarly embedded small translation generalized quadrangles. 13.5. Nonplanarly embedded translation generalized quadrangles
13 editions published in 2006 in English and held by 1,509 WorldCat member libraries worldwide
1. Generalized quadrangles. 1.1. Finite generalized quadrangles. 1.2. Automorphisms. 1.3. Grids and dual grids. 1.4. The classical generalized quadrangles. 1.5. The generalized quadrangles T[symbol](O) and T[symbol](C) of tits. 1.6. The generalized quadrangles T[symbol](O). 1.7. Orders of the known generalized quadrangles. 1.8. Generalized quadrangles with small parameters  2. Regularity, antiregularity and 3regularity. 2.1. Regularity. 2.2. Regularity and dual nets. 2.3. Antiregularity. 2.4. Antiregularity and Laguerre planes. 2.5. 3regularity. 2.6. 3regularity and subquadrangles. 2.7. 3regularity, inversive planes, and characterizations  3. Elation and translation generalized quadrangles. 3.1. Some notions from group theory. 3.2. Elation generalized quadrangles. 3.3. Translation generalized quadrangles. 3.4. The kernel of a translation generalized quadrangle. 3.5. T(n,m,q)s and translation generalized quadrangles. 3.6. Regular pseudoovals and regular pseudoovoids. 3.7. Automorphisms of translation generalized quadrangles. 3.8. Important properties of O(n,m,q). 3.9. Pseudoovals. 3.10. Eggs. 3.11. The stabilizer of the basepoint of a translation generalized quadrangle. 3.12. Structure of the automorphism group of a translation quadrangle  4. Generalized quadrangles and flocks. 4.1. Flocks. 4.2. Flocks and translation planes. 4.3. Flocks of ovoids and hyperbolic quadrics. 4.4. Flocks of cones. 4.5. Semifield flocks. Known examples of semifield flocks. 4.6. Generalized quadrangles and flocks. 4.7. Semifield flocks and translation generalized quadrangles. 4.8. Derivation and BLTsets. 4.9. Constructions. 4.10. Property (G) for generalized quadrangles of order (s,s[symbol]). 4.11. Flocks, subquadrangles and ovals. Addendum A: isomorphisms of flock quadrangles and associated geometries. 4.12. The fundamental theorem of qclan geometry, and applications. Addendum B: Basic questions on elation groups. 4.13. The standard conjectures and questions. 4.14. Some results by Payne and K. Thas. 4.15. Elation generalized quadrangles with nonisomorphic elation groups  5. Good eggs. 5.1. Good eggs and good translation generalized quadrangles. 5.2. Good eggs and veronese surfaces. 5.3. Coordinatization and applications  6. Generalized quadrangles, nets and the axiom of Veblen. 6.1. Generalized quadrangles and the axiom of Veblen. 6.2. Translation generalized quadrangles and the axiom of Veblen. 6.3. Property (G) and the axiom of Veblen. 6.4. Flock generalized quadrangles and the axiom of Veblen. 6.5. Subquadrangles and the axiom of Veblen. 6.6. Nets and characterizations of translation generalized quadrangles  7. Ovoids and subquadrangles. 7.1. Ovoids of Q(4,q). 7.2. Subquadrangles and ovoids. 7.3. Translation ovoids and semifield flocks. 7.4. Coordinates of the known nonclassical ovoids of Q(4,q). 7.5. Subquadrangles of T(O), with O good: the even case. 7.6. Subquadrangles of T(O), with O good: the odd case. 7.7. Subquadrangles: remaining cases and some applications. 7.8. Translation generalized quadrangles with one classical subquadrangle. 7.9. Elation generalized quadrangles with a subquadrangle  8. Translation generalized ovals. 8.1. Translation generalized ovoids and translation generalized ovals. 8.2. Note on the definition of translation generalized oval/ovoid. 8.3. Characterizations of the T2 (O) of tits. 8.4. A characterization of translation generalized ovals. 8.5. Classification of 2transitive generalized ovals in even characteristic  9. Moufang sets and translation Moufang sets. 9.1. Definition and general results. 9.2. Finite Moufang sets  10. Configurations of translation points. 10.1. Spansymmetric generalized quadrangles. 10.2. Groups admitting a 4Gonal basis. 10.3. SPGQs and Moufang sets. 10.4. Basic structural Lemmas. 10.5. Classification of SPGQs of order (s,t),1<s[symbol]t<s[symbol]. 10.6. SPGQs of order (s,s[symbol]). 10.7. Generalized quadrangles with a line of translation points. 10.8. On the classification of translation generalized quadrangles  11. Moufang quadrangles with a translation point. 11.1. Notation. 11.2. Some general elementary Lemmas. 11.3. The Moufang property and analogues. 11.4. Tits generalized quadrangles and tits systems. 11.5. Properties of Moufang quadrangles. 11.6. Half 3Moufang quadrangles. 11.7. 2Moufang quadrangles and FongSeitz quadrangles. 11.8. Conclusion  12. Translation ovoids in translation quadrangles. 12.1. Ovoids, elation or translation with respect to a flag or a point. 12.2. Selfpolar elation generalized quadrangles. 12.3. SuzukiTits Moufang sets. 12.4. Subtended elation ovoids  13. Translation generalized quadrangles in projective space. 13.1. Generalities about Lax embeddings. 13.2. Planar translationhomogeneous embeddings. 13.3. Exceptional nonplanar translationhomogeneous embeddings. 13.4. Nonplanarly embedded small translation generalized quadrangles. 13.5. Nonplanarly embedded translation generalized quadrangles
Absolute arithmetic and F1geometry by
Koen Thas(
)
10 editions published between 2014 and 2016 in English and Undetermined and held by 537 WorldCat member libraries worldwide
It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, F₁, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the DeningerManin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the F₁world, covers several areas in F₁theory, and is divided into four main parts  Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind F₁, categorical foundations, the blend of different scheme theories over F₁ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality
10 editions published between 2014 and 2016 in English and Undetermined and held by 537 WorldCat member libraries worldwide
It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, F₁, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the DeningerManin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the F₁world, covers several areas in F₁theory, and is divided into four main parts  Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind F₁, categorical foundations, the blend of different scheme theories over F₁ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality
Symmetry in finite generalized quadrangles by
Koen Thas(
Book
)
12 editions published between 2004 and 2010 in English and German and held by 246 WorldCat member libraries worldwide
In this monograph finite generalized quadrangles are classified by symmetry, generalizing the celebrated LenzBarlotti classification for projective planes. The book is selfcontained and serves as introduction to the combinatorial, geometrical and grouptheoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, spansymmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BNpairs of rank 1, and the Moufang property
12 editions published between 2004 and 2010 in English and German and held by 246 WorldCat member libraries worldwide
In this monograph finite generalized quadrangles are classified by symmetry, generalizing the celebrated LenzBarlotti classification for projective planes. The book is selfcontained and serves as introduction to the combinatorial, geometrical and grouptheoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles, including automorphism groups, elation and translation generalized quadrangles, generalized ovals and generalized ovoids, spansymmetric generalized quadrangles, flock geometry and property (G), regularity and nets, split BNpairs of rank 1, and the Moufang property
A course on elation quadrangles by
Koen Thas(
Book
)
9 editions published in 2012 in English and held by 127 WorldCat member libraries worldwide
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 pmodular cohomology, Heisenberg groups and existence problems for certain translation nets, are briefly touched. The text starts from scratch and is essentially selfcontained. 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
9 editions published in 2012 in English and held by 127 WorldCat member libraries worldwide
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 pmodular cohomology, Heisenberg groups and existence problems for certain translation nets, are briefly touched. The text starts from scratch and is essentially selfcontained. 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
Singer quadrangles(
)
1 edition published in 2009 in English and held by 15 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 15 WorldCat member libraries worldwide
Translation generalized quadrangles by
J. A Thas(
Book
)
1 edition published in 2006 in English and held by 10 WorldCat member libraries worldwide
1 edition published in 2006 in English and held by 10 WorldCat member libraries worldwide
Categoric aspects of authentication by
Jeroen Schillewaert(
Book
)
3 editions published in 2012 in English and German and held by 5 WorldCat member libraries worldwide
3 editions published in 2012 in English and German and held by 5 WorldCat member libraries worldwide
Singer quadrangles by Stefaan de Winter(
Book
)
1 edition published in 2009 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2009 in English and held by 3 WorldCat member libraries worldwide
Classification of finite generalized quadrangles by
Koen Thas(
Book
)
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 2 WorldCat member libraries worldwide
Translation generalized quadrangles by
J. A Thas(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Translation Generalized Quadrangles. Series in Pure Mathematics, Volume 26(
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Automorphisms and combinatorics of finite generalized quadrangles by
Koen Thas(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
Absolute Arithmetic and $\mathbb F_1$Geometry(
)
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, $\mathbb F_1$, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the DeningerManin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the $\mathbb F_1$world, covers several areas in $\mathbb F_1$theory, and is divided into four main parts  Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind $\mathbb F_1$, categorical foundations, the blend of different scheme theories over $\mathbb F_1$ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality
1 edition published in 2016 in English and held by 1 WorldCat member library worldwide
It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, $\mathbb F_1$, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the DeningerManin program, which aims at solving the classical Riemann Hypothesis. This book, which is the first of its kind in the $\mathbb F_1$world, covers several areas in $\mathbb F_1$theory, and is divided into four main parts  Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic. Topics treated include the combinatorial theory and geometry behind $\mathbb F_1$, categorical foundations, the blend of different scheme theories over $\mathbb F_1$ which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic. Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way. The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality
Notes on elation generalized quadrangles(
)
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
1 edition published in 2002 in English and held by 1 WorldCat member library worldwide
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