1,354,306 research outputs found
The Ghinelli-Loewe construction of generalized quadrangles
No full textIn 1994 Ghinelli and Lowe announced an abstract construction of finite generalized quadrangles (GQ) of order (q^2,q) where q=p^{2n}, p a prime. With a computer search they actually obtained several examples with p=3(mod4) and n=1.In this paper we offer a brief summary of the construction and an indication of the proof that the examples actually produced are of Kantor-Knuth type whose point-line duals are translation GQ of dimension 2 over their kernel
Affine attenuated spaces
No full textWe prove that a rank d geometry satisfying the “Intersection Property” and belonging to the diagram with s > 3 and d ⩾ 4 is isomorphic to an affine attenuated space (i.e., the geometry of the subspaces of a projective space not meeting a given subspace and not contained in a fixed hyperplane)
Locally partial geometries with different types of residues
No full textA class of locally partial geometries (L.pGs for short) is constructed where both linear spaces and generalized quadrangles occur as point-residues. We conjecture that this class gives all possible example of L.pGs with that anomaly. We prove this conjecture when plane-residues are projective planes (see section 5). In the general case, we are able to prove the conjecture when there is at least one point with a linear residue, satisfying an additional assumption. © 1992, Elsevier B.V. All rights reserved
Characterization of some 4-gonal configurations of AHRENS-SZEKERES type
No full textMotivated by the Ahrens-Szekeres-Quadrangles I present a variation of the 4-gonal families method of construction introduced by Kantor in 1980. Since a long time it has been known the relation between generalized quadrangles of order (s,s) and of order (s-1,s+1). A geometrical description of this interrelation was given by Payne in 1971 and rests on the notion of regular points or rather of regular lines. In this paper I develop these connections algebraically in the hope of getting more insight into them from the group theoretical point of view. In this way I am able to characterize two classes of known 4-gonal configurations
Projective planes with a large quasi-regular collineation group
No full textLondon Mathematical Society Lecture Note Series n. 307
Let be a finite projective plane of order n, and let G be a large
abelian (or, more generally, quasiregular) collineation group of ; to
be specific, we assume |G| > (n2 + n + 1)/2. Such planes have been
classified into eight cases by Dembowski and Piper in 1967. We survey
the present state of knowledge about the existence and structure of such
planes. We also discuss some geometric applications, in particular to the
construction of arcs and ovals. Technically, a recurrent theme will be
the amazing strength of the approach using various types of difference
sets and the machinery of integral group rings
Characterization of some 4-gonal configurations of Ahrens–Szekeres type
No full textMotivated by the Ahrens–Szekeres Quadrangles, we shall present a variation of the 4-gonal family method of construction introduced by Kantor in 1980. The relation between generalized quadrangles of order (s, s) and of order (s − 1, s + 1) has been known for a long time. A geometrical description of this interrelation was given by Payne in 1971 and rests on the notion of regular points or of regular lines. In this paper we wish to develop these connections algebraically in the hope of getting more insight into them from the group-theoretical point of view. In this way we are able to characterize two classes of known 4-gonal configurations
A non-existence result for finite projective planes in Lenz-Barlotti class I.4
No full textLet Pi be a projective plane of order n in Lenz-Barlotti class I.4, and assume that n is a multiple of 3. Then either n=3 or n is a multiple of 9
Maria Venturi e Lorenza Ghinelli: un ottimismo incauto?
No full textThis is the author accepted manuscript. The final version is available from Taylor & Francis via the DOI in this recordTra il 1987 e il 2017 Maria Venturi e Lorenza Ghinelli, autrici di grande successo commerciale,
hanno scritto molte storie sull’abuso sessuale dei minori. In alcuni casi hanno mostrato una seria
comprensione degli aspetti dannosi di una simile esperienza, ma in altri casi l’hanno descritta in
modi che ne attenuano la traumaticità. Questo articolo riconosce l’aspetto incoraggiante che le
storie di eventi dolorosi possono avere; segnala la difficoltà di trovare quell’aspetto nelle storie
di abuso sessuale; sostiene che un incoraggiamento efficace non può essere trovato a spese di
una rappresentazione realistica; e nota l’insolito valore che la verosomiglianza assume allora
come criterio valutativo delle storie di abuso sessuale
Some geometric aspects of finite abelian group
No full textLet Π be a finite projective plane admitting a large abelian collineation group. It is well known that this situation may be studied by algebraic means (via a representation by suitable types of difference sets), namely using group rings and algebraic number theory and leading to rather strong nonexistence results. What is less well-known is the fact that the abelian group (and sometimes its group ring) can also be used in a much more geometric way; this will be the topic of the present survey. In one direction, abelian collineation groups may be applied for the construction of interesting geometric objects such as unitals, arcs and (hyper-)ovals, (Baer) subplanes, and projective triangles. On the other hand, this approach makes it sometimes possible to provide simple geometric proofs for non-trivial structural restrictions on the given collineation group, avoiding algebraic machinery
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