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Titlebook: q-Clan Geometries in Characteristic 2; Ilaria Cardinali,Stanley E. Payne Book 2007 Birkhäuser Basel 2007 Dimension.automorphism group.boun

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发表于 2025-3-21 19:49:52 | 显示全部楼层 |阅读模式
书目名称q-Clan Geometries in Characteristic 2
编辑Ilaria Cardinali,Stanley E. Payne
视频video
概述Includes supplementary material:
丛书名称Frontiers in Mathematics
图书封面Titlebook: q-Clan Geometries in Characteristic 2;  Ilaria Cardinali,Stanley E. Payne Book 2007 Birkhäuser Basel 2007 Dimension.automorphism group.boun
描述.A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely..
出版日期Book 2007
关键词Dimension; automorphism group; boundary element method; character; discrete geometry; fundamental theorem
版次1
doihttps://doi.org/10.1007/978-3-7643-8508-8
isbn_softcover978-3-7643-8507-1
isbn_ebook978-3-7643-8508-8Series ISSN 1660-8046 Series E-ISSN 1660-8054
issn_series 1660-8046
copyrightBirkhäuser Basel 2007
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Other Good Stuff,eal and have a wide variety of connections with other geometric objects. For a general reference see J. A. Thas and S. E. Payne [TP94]. For . = 2e see especially [BOPPR1] and [BOPPR2]. In this section we give a very brief introduction to the material contained in these latter two papers.
发表于 2025-3-22 06:00:47 | 显示全部楼层
Book 2007sarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives
发表于 2025-3-22 09:36:27 | 显示全部楼层
The Adelaide Oval Stabilizers, which acts on the points of this line as (0, .) ↦ (0, y2/δ, ., from which it follows that exactly three points on this line are fixed: the oval point (0, ., 1) and two others: (0, 1, 0) and (0, 0, 1). But the secant line through . and . passes through the point (0, 1, 0), implying that the nucleus must be (0, 0, 1).
发表于 2025-3-22 16:18:11 | 显示全部楼层
Book 2007 a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals are worked out completely..
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The Payne q-Clans,98] show that up to the usual equivalence of .-clans, the three known examples are the only ones. Since the two non-classical families exist only for . odd, we assume throughout this chapter that . is odd. Then the three known families have the following appearance. There is some positive integer .
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