1,720,992 research outputs found
On collineation groups of finite projective spaces containing a Singer cycle
No full textBy a result of W.M. Kantor, any subgroup of GL(n,q) containing a Singer cycle normalizes a field extension subgroup.
This result has as a consequence a projective analogue, and this paper gives the details of this deduction, showing that any subgroup of PGammaL(n,q) containing a projective Singer cycle normalizes the image of a field extension subgroup GL(n/s,q^s) under the canonical homomorphism GL(n,q)\rightarrow \PGL(n-1,q), for some divisor s of n, and so is contained in the image of GammaL(n/s,q^s) under the canonical homomorphism GammaL(n,q)\rightarrow\PGammaL(n-1,q). The actions of field extension subgroups on V(n,q) are also investigated. In particular, we prove that any field extension subgroup GL(n/s,q^s) of GL(n,q) has a unique orbit on s-dimensional subspaces of V(n,q) of length coprime to q. This orbit is a Desarguesian s-partition of V(n,q)
On the incidence map of incidence structures
Get PDFBy using elementary linear algebra methods we exploit properties of the incidence map of certain incidence structures with finite block sizes. We give new and simple proofs of theorems of Kantor and Lehrer, and their infinitary version. Similar results are obtained also for diagrams geometries.
By mean of an extension of Block’s Lemma on the number of orbits of an automorphism group of an incidence structure, we give informations on the number of orbits of: a permutation group (of possible infinite degree) on subsets of finite size; a collineation group of a projective and affine space (of possible infinite dimension) over a finite field on subspaces of finite dimension; a group of isometries of a classical polar space (of possible infinite rank) over a finite field on totally isotropic subspaces (or singular in case of orthogonal spaces) of finite dimension.
Furthermore, when the structure is finite and the associated incidence matrix has full rank, we give an alternative proof of a result of Camina and Siemons. We then deduce that certain families of incidence structures have no sharply transitive sets of automorphisms acting on blocks
Bol quasifields
Get PDFIn the context of configurational characterisations of symmetric projective
planes, a new proof of a theorem of Kallaher and Ostrom characterising planes of even order of Lenz-Barlotti type IV.a.2 via Bol conditions is given. In contrast to their proof,we need neither the Feit-Thompson theorem on solvability of groups of odd order, nor Bender’s strongly embedded subgroup theorem, depending rather on Glauberman’s Z*-theorem
The action of the group G2(q) < PSU6(q2), q even, and related combinatorial structures
No full textWe describe some geometrical properties of the action of the Cartan-Dickson-Chevalley exceptional group G2(q), q even, as a subgroup of the unitary group PSU6(q^2).This allows us to provide a new description of the known 126-hyperoval of H(5,4) and to construct even subsets of PG(2,q ^2)
Classification of flocks of the quadratic cone in PG(3,64)
Get PDFFlocks are an important topic in the field of finite geometry, with many
relations with other objects of interest. This paper is a contribution to the
difficult problem of classifying flocks up to projective equivalence. We
complete the classification of flocks of the quadratic cone in PG(3,q) for q <=
71, by showing by computer that there are exactly three flocks of the quadratic
cone in PG(3,64), up to equivalence. The three flocks had previously been
discovered, and they are the linear flock, the Subiaco flock and the Adelaide
flock. The classification proceeds via the connection between flocks and herds
of ovals in PG(2,q), q even, and uses the prior classification of hyperovals in
PG(2,64)
Relative symplectic subquadrangle hemisystems of the Hermitian surface
No full textWe introduce the notion of relative subquadrangle regular system of a generalized quadrangle. A relative subquadrangle regular system of order m on a generalized quadrangle S of order (s, t) is a set R of embedded subquadrangles with a prescribed intersection prop- erty with respect to a given subquadrangle T such that every point of S \ T lies on exactly m subquadrangles of R. If m is one half of the total number of such subquadrangles on a point we call R a relative subquadrangle hemisystem with respect to T . We construct two infinite families of symplectic relative subquadrangle hemisystems of the Hermitian surface H(3,q2), q even
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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