A New Family of Extended Generalized Quadrangles of Order (q+ 1,q− 1)
نویسندگان
چکیده
منابع مشابه
Elation Generalized Quadrangles of order ( q 2 ; q ) Christine
We survey some recent classiication theorems for elation generalized quadrangles of order (q 2 ; q); q even, with particular emphasis on those involving subquadrangles of order q.
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In addition to the generalized quadrangles arising naturally from smalldimensional symplectic, unitary, or orthogonal geometries, the only known finite examples are the following quadrangles and their duals: ones with parameters 4, 4 (where 4 = 2e > 8) or q*, 4 (where q = 22e+l > 8) due to Tits [4, p. 3041; and others with parameters q 1, q + 1 (for prime powers q) due to Hall [5] and Ahrens an...
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To Professor Helmut Wielandt, to commemorate his seventy-fifth birthday 1. Introduction In [2] a new generalized quadrangle with parameters q2, q was constructed using the G 2(q) generalized hexagon (q == 2 (mod 3), q > 2). In addition, an elementary group theoretic technique was presented for constructing generalized quadrangles. This technique was refined by Payne [3] in order to simplify cal...
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Given a finite generalized quadrangle Q, an extended generalized quadrangle is called an extension of Q if each point-residue is isomorphic to Q. There are several known examples of extended generalized quadrangles [4, §1.1], among which those admitting flag-transitive automorphism groups have been extensively studied in their close relations with group theory. Those flag-transitive geometries ...
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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: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0345