1,720,966 research outputs found
Generation of finite groups and maximal subgroup growth
Full text linkLet G be a finite group and, for n (Formula Presented) N, denote by mn (G) the number of maximal subgroups of G with index n. Let (Formula Presented] and let E1 (G) be the expected number of elements of G which have to be drawn at random, with replacement, before a set of generators is found. Then (Formula Presented)
A probabilistic version of a theorem of Laszlo Kovacs and Hyo-Seob Sim
Full text linkFor a finite group group, denote by V(G) the smallest positive integer k with the property that the probability of generating G by k randomly chosen elements is at least 1/e. Let G be a finite soluble group. Assume that for every p ∈ π(G) there exists Gp ≤ G such that p does not divide |G: Gp | and V(Gp) ≤ d. Then V(G) ≤ d + 7
Primitive permutation IBIS groups
Full text linkLet G be a finite permutation group on Ω. An ordered sequence of elements of Ω, (ω1,...,ωt), is an irredundant base for G if the pointwise stabilizer G(ωjavax.xml.bind.JAXBElement@606ca359,...,ωjavax.xml.bind.JAXBElement@77e0dd48) is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of G have the same size we say that G is an IBIS group. In this paper we show that if a primitive permutation group is IBIS, then it must be almost simple, of affine-type, or of diagonal type. Moreover we prove that a diagonal-type primitive permutation groups is IBIS if and only if it is isomorphic to PSL(2,2f)×PSL(2,2f) for some f≥2, in its diagonal action of degree 2f(22f−1)
Bounding the maximal size of independent generating sets of finite groups
Full text linkDenote by m(G) the largest size of a minimal generating set of a finite group G. We estimate m(G) in terms of Σpεπ(G) dp(G), where we are denoting by dp(G) the minimal number of generators of a Sylow p-subgroup of G and by π(G) the set of prime numbers dividing the order of G
The Tarski irredundant basis theorem and the finite soluble groups
No full textDenote by d=d(G) and m=m(G), respectively, the smallest and the largest cardinality of a minimal generating set of a finite group G. The Tarski irredundant basis theorem implies that for every k with d(G)<=
Boolean lattices in finite alternating and symmetric groups
Full text linkGiven a group G and a subgroup H, we let denote the lattice of subgroups of G containing H. This article provides a classification of the subgroups H of G such that is Boolean of rank at least when G is a finite alternating or symmetric group. Besides some sporadic examples and some twisted versions, there are two different types of such lattices. One type arises by taking stabilisers of chains of regular partitions, and the other arises by taking stabilisers of chains of regular product structures. As an application, we prove in this case a conjecture on Boolean overgroup lattices related to the dual Ore's theorem and to a problem of Kenneth Brown
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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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