Classification of extended generalized quadrangles with maximum diameter
نویسندگان
چکیده
منابع مشابه
Classification of skew translation generalized quadrangles, I
Generalized n-gons were introduced by Tits in a famous work on triality [20] of 1959, in order to propose an axiomatic and combinatorial treatment for semisimple algebraic groups (including Chevalley groups and groups of Lie type) of relative rank 2. They are the central rank 2 incidence geometries, and the atoms of the more general “Tits-buildings.” If the number of elements of a generalized n...
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Suppose S is a finite generalized quadrangle (GQ) of order (s, t), s 6= 1 6= t, and suppose that L is a line of S. A symmetry about L is an automorphism of the GQ which fixes every line of S meeting L (including L). A line is called an axis of symmetry if there is a full group of symmetries of size s about this line, and a point of a generalized quadrangle is a translation point if every line t...
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We tell the history ofMoufang generalized quadrangles.We review someMoufang-like conditions, and classify finite quasi-transitive generalized quadrangles. These are generalized quadrangles so that for any two non-concurrent linesU,V of theGQ, and for someW ∈ {U,V }⊥, the group of generalized homologies with axes U and V acts transitively on the points ofW incident with neither U nor V. As a by-...
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A line L of a finite generalized quadrangle S of order ðs; tÞ, s; t > 1, is an axis of symmetry if there is a group of full size s of collineations of S fixing any line which meets L. If S has two non-concurrent axes of symmetry, then S is called a span-symmetric generalized quadrangle. We prove the twenty-year-old conjecture that every span-symmetric generalized quadrangle of order ðs; sÞ is c...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1992
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90128-3