Results 1 to 10 of about 78 (71)
Classification of skew translation generalized quadrangles, I [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Combinatorics
Koen Thas
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A translation generalized quadrangle in characteristic ≠0 is linear [PDF]
Advances in Mathematics, 2019 It is a long-standing conjecture from the 1970s that every translation generalized quadrangle is linear, that is, has an endomorphism ring which is a division ring (or, in geometric terms, that has a projective representation). We show that any translation generalized quadrangle $Γ$ is ideally embedded in a translation quadrangle which is linear.
Koen Thas
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Parameters of translation generalized quadrangles
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2005 The author considers triples \((E,{\mathcal O}, T)\) where \(E\) is a group, \({\mathcal O}\) a set of subgroups, and \(T\) maps any \(A\in {\mathcal O}\) to a subgroup \(T_A\) containing \(A\). Such a triple is called a fourgonal family, if certain additional axioms hold.
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Translation ovoids of flock generalized quadrangles
European Journal of Combinatorics, 2004 Let \(S(F)\) be the generalised quadrangle (GQ) of order \((q^2,q)\) as defined by the fourgonal family \(F\). A translation ovoid \(O\) of \(S(F)\) is a set of \(q^3+1\) points of \(S(F)\) such that: (1) no two points of \(O\) are collinear on \(S(F)\); (2) \((\infty)\in O\) and there is a subgroup of the elation group \(G\) fixing \((\infty)\) which ...
BADER, LAURA, TROMBETTI, ROCCO
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A stabilizer lemma for translation generalized quadrangles
European Journal of Combinatorics, 2007 Let \(F\) be a semifield flock of the finite projective space \(\text{PG}(3,q^n)\), where \(q\) is odd. The author proves that \(F\) is linear if the order of the automorphism group of \(F\) is divisible by \(q^n (q^n +1)\). As a consequence, he obtains the following result for a certain class of translation generalized quadrangles \(S\) of order \((s,
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Generalized quadrangles of order (s,s2). IV Translations, Moufang and Fong-Seitz
Discrete Mathematics, 2023 In the period 1994-1999 Thas wrote a series of three papers on generalized quadrangles of order $(s, s^2)$. In this Part IV we classify all finite translation generalized quadrangles of order $(s, s^2)$ having a kernel of size at least 3, containing a regular line not incident with the translation point.
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TRANSLATION GENERALIZED QUADRANGLES FOR WHICH THE TRANSLATION DUAL ARISES FROM A FLOCK [PDF]
Glasgow Mathematical Journal, 2003 It is shown that each finite translation generalized quadrangle (TGQ) $\mathcal{S}$, which is the translation dual of the point-line dual of a flock generalized quadrangle, has a line $[\infty]$ each point of which is a translation point. This leads to the fact that the full group of automorphisms of $\mathcal{S}$ acts $2$-transitively on the points of
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Translation Generalized Quadrangles of Order (s,s2), s Even, and Eggs
Journal of Combinatorial Theory, Series A, 2002 An egg \(O(n,2n,q)\) of \(PG(4n-1,q)\) is a set of \(q^{2n}+1\) \((n-1)\)-dimensional subspaces \(PG^{(i)}(n-1,q)\), \(i=0,\ldots,q^{2n}\), any three of which generate a \(PG(3n-1,q)\) and such that every element \(PG^{(i)}(n-1,q)\) of \(O(n,2n,q)\) is contained in a \(PG^{(i)}(3n-1,q)\) having no point in common with any element \(PG^{(j)}(n-1,q)\), \(
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Designs, Codes and CryptographyAbstractWe provide classification results for translation generalized quadrangles of order less than or equal to 64, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in $$\textrm{PG}(3n-1,2)$$ PG ( 3
Monzillo G., Penttila T., Siciliano A.
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Relationship between Cervical Instability in the Course of Rheumatoid Arthritis and Pelvic Parameters of Sagittal Balance. [PDF]
J Clin Med, 2023 Wróblewski R +4 more
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