Buildings and Classical Groups
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This requires a completely different approach, using tools from the representation theory of quasisimple groups. Locally elusive classical groups.
N2 - Let G be a transitive permutation group of degree n with point stabiliser H and let r be a prime divisor of n. AB - Let G be a transitive permutation group of degree n with point stabiliser H and let r be a prime divisor of n.
Project : Research. Locally elusive classical groups Timothy C. School of Physics, Maths and Computing. Abstract Let G be a transitive permutation group of degree n with point stabiliser H and let r be a prime divisor of n. Fingerprint Classical Groups.
Buildings of classical groups and centralizers of Lie algebra elements
Primitive Group. Permutation group. Simple group. Representation Theory.
Israel Journal of Mathematics , 1 , SearchWorks Catalog Stanford Libraries. Diagram geometry : related to classical groups and buildings. Responsibility Francis Buekenhout, Arjeh M. Imprint Berlin : Springer, c Physical description xiii, pages : illustrations ; 25 cm.
Series Ergebnisse der Mathematik und ihrer Grenzgebiete 3.
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:عنوان Diagram geometry : related to classical groups and buildings |اف ایی
Find it at other libraries via WorldCat Limited preview. Contributor Cohen, Arjeh M. Bibliography Includes bibliographical references and index. Contents Geometries. The concept of a geometry ; Incidence systems and geometries ; Homomorphisms ; Subgeometries and truncations ; Residues ; Connectedness ; Permutation groups ; Groups and geometries ; Exercises ; Notes Diagrams. From a geometry to a chamber system ; Residues ; From chamber systems to geometries ; Connectedness ; The diagram of a chamber system ; Groups and chamber systems ; Exercises ; Notes Thin geometries.
The affine space of a Vector space ; The Projective space of a Vector space ; Matroids ; Matroids from geometries ; Steiner systems ; Geometries related to the golay code ; Exercises ; Notes Projective and affine spaces. Perspectivities ; Projective lines ; Classification of projective spaces ; Classification of affine spaces ; Apartments ; Grassmannian geometry ; Root filtration spaces ; Exercises ; Notes Polar spaces.
Duality for geometries over a linear diagram ; Duality and sesquilinear forms ; Absolutes and reflexive sesquilinear forms ; Polar spaces ; The diagram of a polar space ; From diagram to space ; Singular subspaces ; Other shadow spaces of polar geometries ; Root filtration spaces ; Polar spaces with thin lines ; Exercises ; Notes Projective embeddings of polar spaces. Geometric hyperplanes and ample connectedness ; The Veldkamp space ; Projective embedding for rank at least four ; Projective embedding for rank three ; Automorphisms of polar spaces ; Exercises ; Notes Embedding polar spaces in absolutes.
Embedded spaces ; Collars and tangent hyperplanes ; A Quasi-polarity ; Technical results on division rings ; Embedding in 3-dimensional space ; Exercises ; Notes Classical polar spaces. Building axioms ; Properties of buildings ; Tits systems ; Shadow spaces ; Parapolar spaces ; Root shadow spaces ; Recognizing shadow spaces of buildings ; Exercises ; Notes References Index.
Summary This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries related to Coxeter groups and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples.