Titlebook: Generalized Polygons; Hendrik Maldeghem Book 1998 Springer Basel AG 1998 Geometry.3D.3D graphics.algebraic topology.character.classificati

Soliloquy

Ovoids, Spreads and Self-Dual Polygons,spaces sometimes produce ovoids in these spaces, and likewise polarities in generalized polygons sometimes produce ovoids in the polygons). Another feature of ovoids is that they sometimes have interesting automorphism groups. The Suzuki groups and the Ree groups of characteristic 2 arise in that wa

adipose-tissue

Projectivities and Projective Embeddings,**c], . [1996] and . & . [19**a], [19**b]. The proofs where hexagons are involved use some very technical results about certain point sets in finite projective spaces, and this is beyond the scope of this book. Where finite generalized quadrangles are involved, one again uses the results of . & . [1

condescend

cogent

Book 1998 and precursors of more general geometries such as partial geometries, partial quadrangles, semi-partial ge­ ometries, near polygons, Moore geometries, etc. The main examples of generalized polygons are the natural geometries associated with groups of Lie type of relative rank 2. This is where group

gonioscopy

敌手

畏缩

Coordinatization and Further Examples,pful in proving numerous results in the classical planes. For generalized polygons, coordinates have helped in proving results in both general and classical polygons. No generalized polygon, apart from many projective planes, was first constructed via coordinatization, but some have otherwise no ele

破裂

The Moufang Condition,r, we aim at a description (but not proof) of a characterization of all these examples. Namely, they are the only polygons satisfying the Moufang condition; see Definitions 4.4.4 on page 143. The main results are due to . [1976a], [1976b], [19**], [1979], [1983], [1994a], . [1979] and . & . [19.]. .

Ankylo-

misshapen

Ovoids, Spreads and Self-Dual Polygons, a set of mutually opposite points “of maximal size” (this will be made precise below for infinite polygons), and the dual notion is a spread. Sets of maxial size with respect to a certain property in geometries usually themselves have interesting properties. For example, they might be used to const