1,720,980 research outputs found
On finite simple groups and Kneser graphs
No full textFor a finite group G let Γ(G) be the (simple) graph defined on the elements of G with an edge between two (distinct) vertices if and only if they generate G. The chromatic number of Γ(G) is considered for various non-solvable groups G
ON THE CLIQUE NUMBER OF THE GENERATING GRAPH OF A FINITE GROUP
No full textThe generating graph Γ(G) of a finite group G is the graph defined on the elements of G with an edge connecting two distinct vertices if and only if they generate G. The maximum size of a complete subgraph in Γ(G) is denoted by ω(G). We prove that if G is a non-cyclic finite group of Fitting height at most 2 that can be generated by 2 elements, then ω(G)=q+1, where q is the size of a smallest chief factor of G which has more than one complement. We also show that if S is a non-abelian finite simple group and G is the largest direct power of S that can be generated by 2 elements, then ω(G)≤(1+o(1))m(S), where m(S) denotes the minimal index of a proper subgroup in S
d-WISE GENERATION OF SOME INFINITE GROUPS
No full textWhat is the largest possible size of a subset of SL(n, Z) from which every pair of elements will be a generating set? We prove a general result on generation probabilities in profinite groups that suggests the cardinality of a maximal such subset equals that of the analogous subset of SL(n, Z/2Z)
On the maximal number of elements pairwise generating the symmetric group of even degree
No full textLet G be the symmetric group of degree n. Let ω(G) be the maximal size of a subset S of G such that 〈x,y〉=G whenever x,y∈S and x≠y and let σ(G) be the minimal size of a family of proper subgroups of G whose union is G. We prove that both functions σ(G) and ω(G) are asymptotically equal to [Formula presented] when n is even. This, together with a result of S. Blackburn, implies that σ(G)/ω(G) tends to 1 as n→∞. Moreover, we give a lower bound of n/5 on ω(G) which is independent of the classification of finite simple groups. We also calculate, for large enough n, the clique number of the graph defined as follows: the vertices are the elements of G and two vertices x,y are connected by an edge if 〈x,y〉≥An.Let G be the symmetric group of degree n. Let omega(G) be the maximal size of a subset S of G such that (x, y) = G whenever x, y E S and x not equal y and let sigma(G) be the minimal size of a family of proper subgroups of G whose union is G. We prove that both functions sigma(G) and omega(G) are asymptotically equal to 1/2(n/n/2) when n is even. This, together with a 2 n/2 result of S. Blackburn, implies that sigma(G)/omega(G) tends to 1 as n ->infinity. Moreover, we give a lower bound of n/5 on omega(G) which is independent of the classification of finite simple groups. We also calculate, for large enough n, the clique number of the graph defined as follows: the vertices are the elements of G and two vertices x, y are connected by an edge if (x, y) >= A(n). (C) 2021 Elsevier B.V. All rights reserved
Hamiltonian cycles in the generating graphs of finite groups
No full textFor a finite group G let Gamma(G) denote the graph defined on the non-identity elements of G in such a way that two distinct vertices are connected by an edge if and only if they generate G. In this paper it is shown that the graph Gamma(G) contains a Hamiltonian cycle for many finite groups G
Some results and questions related to the generating graph a finite group
No full textFor a finite group G a graph Gamma(G) is defined on the
elements of G in such a way that two distinct vertices are
connected by an edge if and only if they generate G.Some
results and questions are given about Gamma(G). This article is
much focused on the relationship between two invariants associated to the graph Gamma(G): the clique number and the chromatic number
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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