Top PDF Certain finite abelian groups with the Redei k-property

Certain finite abelian groups with the Redei k-property

Certain finite abelian groups with the Redei k-property

A factorization is called normalized if each of its factors is a normalized subset. A subset A of G is defined to periodic if there is a g ∈ G \ {e} for which gA = A. A factorization is defined to be periodic if at least one its factors is periodic. A finite abelian group possesses the Haj´os k-property if it admits only periodic factorizations into k factors. For a subset A of G the notation hAi stands for the smallest subgroup of G that contains A, that is, hAi denotes the span of A in G. A normalized subset A of G is called a full-rank subset if hAi = G. In other words the normalized subset A of G is a full-rank
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Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes

Groups whose proper subgroups of infinite rank have polycyclic-by-finite conjugacy classes

Belyaev and Sesekin characterized minimal non-F C-groups when they have a non-trivial finite or abelian factor group. They proved that such minimal non-F C-groups are finite cyclic extensions of divisible abelian p-groups of finite rank, where p is a prime, hence they are Chernikov groups. In [4] it is proved, for groups having a proper subgroup of finite index, that the property of being a minimal non-(P F )C-group is equivalent to that of being a minimal non-F C-group. Note that in [4], the property (P F )C was denoted by P C. Since in [9], groups with polycyclic conjugacy classes have been considered and denoted by P C-groups, it is convenient, to denote in this note, groups with polycyclic-by-finite conjugacy classes by (P F )C-groups. In [9, Theorem A] it is proved that a non- perfect minimal non-P C-group is a minimal non-F C-group. Here we will generalize this last result to non-perfect minimal non-(P F )C-groups. Our first result is the following theorem.
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Groups with all subgroups permutable or soluble

Groups with all subgroups permutable or soluble

The purpose of our paper is to discuss locally graded groups in which all non-permutable subgroups are soluble. Our research has been stimulated by a recent paper of K. Ersoy, A. Tortora and M. Tota [5] who have obtained some nice results concerning locally graded groups in which all non- subnormal subgroups are soluble of bounded derived length and we are indebted to these authors for giving us a preprint of their work. Work in this particular area is trickier for a couple of reasons. Unlike with nilpotent groups, a finite group in which all proper subgroups are soluble need not be soluble. However, J. Thompson [23] has exhibited the finite minimal simple groups–those non-abelian simple groups in which every proper subgroup is soluble. A further problem is that, as yet, the structure of a locally graded group in which every proper subgroup is soluble is not fully understood, although in [7] it is shown that such groups are hyperabelian.
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Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov

Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov

Finally, let G be a group that satisfies the hypotheses of (e) and suppose first that G/Z(N ) is nilpotent. We claim that X := Z(N ) ≤ Z(G), and assuming this false we have by residual nilpotency that [X, G, G] < [X, G], so that we may factor and hence assume that [X, G, G] = 1. Choose an element a of X that has order p modulo Z(G), and consider the homomorphism θ : G → [X, G] given by θ(g) = [a, g] for all g ∈ G. The image of θ has exponent exactly p, but G/ ker(θ) is divisible and we have a contradiction that establishes the claim. It remains only to show that G/X is residually nilpotent, for then by induction on the class of N we may assume G/X nilpotent and hence G nilpotent, by the above. Since G/N is a divisible Baer p-group and hence abelian, there is a set {K λ : λ ∈ Λ} of G-invariant subgroups of N with trivial intersection such that each G/K λ is
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art A.M.P.de Carvalho

art A.M.P.de Carvalho

O Estado ajustador, em um confronto explícito como o padrão do Estado democrático, isenta-se, pro- gressivamente, do seu papel de garantidor de direitos, concretizando-se, assim, um encolhimento de suas responsabilidades sociais. Com efeito, um fenômeno- chave nessa nova ordem do capital é a desconstrução dos direitos que assume, então, uma dupla dimensão: a primeira é a erosão real dos direitos. Nesse contexto, direitos do trabalho são destituídos e redei nidos; di- reitos sociais não conseguiram consolidar suas garan- tias; direitos historicamente conquistados são negados ou fragmentados, coni gurando-se, desse modo, o desmonte dos serviços sociais. A outra dimensão é a erosão da própria noção de direitos e das referências pelas quais os direitos podem ser formulados. É o en- colhimento do horizonte da legitimidade dos direitos. Vivencia-se a dii culdade ou a impossibilidade de se- rem formulados como demanda, experimentando-se, mesmo, um mal-estar na enunciação dos direitos. E, mais, na ótica da valorização do capital, muitas vezes são tratados como ônus, “contabilizados” – tal como aparece na expressão “custo Brasil”, por exemplo – ou “l exibilizados”, na gramática neoliberal dominante. No mundo do trabalho, vem se operando um esva- ziamento da dimensão fundante do direito; ou seja, o direito deixa de ser uma prerrogativa de todos e se transforma em elemento indexado ao desempenho individual, como “recompensa”. É o direito metamor- foseado em benefício, objeto de retórica, capturado pela racionalidade do Mercado, que retira a “alma do direito”. E, nesta perspectiva, ocorre uma transferência de responsabilidades sociais, também para a socieda- de civil, fazendo ganhar espaço fenômenos como a
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Maximal subgroups of the group PSL(12, 2)

Maximal subgroups of the group PSL(12, 2)

[14] P. B. Kleidman and M. Liebeck,The Subgroup Structure of the Finite Classical Groups, London Mathematical Society Lecture Note Series 129, Cambridge University Press, Cambridge, 1990. MR1057341(91g:20001). Zbl 0697.20004. [15] V. Land´ azuri and G. M. Seitz, On the minimal degrees of projective

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Finite groups, spherical 2-categories, and 4-manifold invariants

Finite groups, spherical 2-categories, and 4-manifold invariants

4-manifold, [M]. For any :$ cohomologous to :, any ;$ cohomologous to ;, and any g : M Ä W(:$) homotopic to f, we have g*( ;$)([M])= f *( ;)([M]). Quinn then takes a certain weighted sum of f *( ;)([M]) over an arbitrary set of representatives of all homotopy classes of maps f. For a precise definition of the weights see [42]. As a matter of fact, Quinn only works out concretely his very abstract construction, which he defines in any dimension, for the classifying space of a finite group and cocycles on that space. In dimension four that corresponds to the restricted case in which H=[1]. The interesting invariants in dimension 4, that we have sketched above, were never considered by Quinn, or anyone else, explicitly. It is clear, by the arguments following our conjecture, that our state-sum invariants for a given semi-weak monoidal structure are equal to Quinn's invariants for the corresponding Postnikov invariants. This shows immediately that our state-sum invariants are homotopy invariants, rather than PL invariants. This is not surprising given the fact that we use finite groups. In dimension 3, the DijkgraafWitten invariants [29] are homotopy invariants as well. As already mentioned, the TuraevViro invariants are real homeomorphism invariants, but they require the use of quantum groups instead of finite groups. The categorical construction that underlies the DijkgraafWitten and the TuraevViro invariants is the same though; it is the specific input in that construction that makes the dif- ference. It is therefore reasonable to look for categorifications of the quan- tum groups, the representations of which could be the right input in our construction, presented in [37], for obtaining true PL invariants. This idea led Crane and Frenkel [23] to the definition of a Hopf category in the first place.
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The comparison of the structure and microhardness of the tool steel C90 and HS 6-5-2 remelted with the electric arc

The comparison of the structure and microhardness of the tool steel C90 and HS 6-5-2 remelted with the electric arc

Machine and tools elements made of the steel C90 and HS 6-5-2 immediately after the conventional hardening, need the tempering process. During the tempering, there is a transforma- tion of retained austenite into martensite and carbides release in martensite, what leads to the increase hardness of the high-speed steel, whereas in non-alloy steels tempering cause decrease the hardness.

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The parts and the whole

The parts and the whole

The thesis is organized as follows: in Chapter 1 we begin our discussion stressing the fact that Non-Contextuality (NC) and Bell inequalities can be expressed as bounds Ω for positive linear combinations S of probabilities of events, S ≤ Ω . Exclusive events in S can be represented as adjacent vertices of a graph called the exclusivity graph of S. In the case that events correspond to the outcomes of quantum projective measurements, quantum probabilities are intimately related to the Grötschel-Lovász-Schrijver theta body of the exclusivity graph. Then, one can efficiently compute an upper bound to the maximum quantum violation of any NC or Bell inequality by optimizing S over the theta body and calculating the Lovász number of the corresponding exclusivity graph. In some cases, this upper bound is tight and gives the exact maximum quantum violation. However, in general, this is not the case. The reason is that the exclusivity graph does not distinguish among the different ways exclusivity can occur in Bell-inequality (and similar) scenarios. An interesting question is whether there is a graph-theoretical concept which accounts for this problem. There we show that, for any given N-partite Bell inequality, an edge-coloured multigraph composed of N single-colour graphs can be used to encode the relationships of exclusivity between each party’s parts of the events. Then, the maximum quantum violation of the Bell inequality is exactly given by a refinement of the Lovász number that applies to these edge-coloured multigraphs. We show how to calculate upper bounds for this number using a hierarchy of semi-definite programs and calculate upper bounds for I 3 , I 3322 and the three bipartite Bell inequalities whose exclusivity
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Back-to-back correlations for finite expanding fireballs

Back-to-back correlations for finite expanding fireballs

Recently, it has been shown [1,2] that large back-to-back correlations (BBC) of particle-antiparticle pairs of bosonic particles might appear in high energy nucleus-nucleus colli- sions as a consequence of in-medium mass modification of the bosons. Detailed calculations indicate that the BBC signal appears for values of transverse momenta below 1–2 GeV/c. More recently, it was shown [3] that BBC of similar strength might appear for fermionic particles as well. The main physical ingredient used in the evaluation of the effects of in-medium modified masses on two particle correlation functions is a quantum-mechanical correlation induced by a nonzero overlap between in-medium and free states. The induced quantum mechanical correlation can be represented in terms of two- mode squeezed states of the asymptotic, observable states and is implemented through a Bogoliubov-Valatin transformation. The possibility of measuring a significant BBC signal in heavy-ion collisions opens new interesting possibilities for accessing the properties of the matter formed in such collisions. The BBC signal is linked to in-medium mass modifications of hadrons in the hot and dense environment the detected particles experience before freezing out and in this sense BBC measurements provide independent pieces of information on medium modifications from the ones obtained from dilepton yields and spectra. However, there are several additional physical effects that interfere with mass modifications of the detected particles in the interpretation of the BBC signal.
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A NEW MULTI PARTY KEY AGREEMENT PROTOCOL USING SEARCH PROBLEMS IN DISCRETE HEISENBERG GROUP.

A NEW MULTI PARTY KEY AGREEMENT PROTOCOL USING SEARCH PROBLEMS IN DISCRETE HEISENBERG GROUP.

In Crypto 2000 [9],Ko et al proposed a new public key cryptosystem based on Braid groups which are non- abelian; they have used the search problems to build the Cryptosystem.Then Paeng et al [13] proposed a New Public Key Cryptosystem using the Discrete Log Problems in inner automorphisms of the semi-direct product of special linear groups (non-abelian) with Zp. The above system was named as MOR cryptosystem.Using Unitriangular[3], and Unimodular matrices, Ayan Mahalonobis[4] modified theMOR cryptosystem .

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Lat. Am. j. solids struct.  vol.11 número14

Lat. Am. j. solids struct. vol.11 número14

The 2D steady-state particular solutions have been incorporated into an in-house standard TFEM code. To validate the numerical implementation, solutions to three test problems are presented below: In the first two, the domain is a simple rectangle; the second involves a curved geometry which may be more representative of an actual system. The analytical solutions are also provided for the purpose of a fair comparison. In each example, eight-node quadratic elements are invoked for discretization and four Gaussian points are utilized along each element side. The particular solutions related to “body force” are approximated using the method of RBFs. Following the work of Qin and Wang (2008), all nodes and elemental centroids are chosen as the reference points in the following numerical examples.
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Braz. J. Phys.  vol.31 número2

Braz. J. Phys. vol.31 número2

symmetry with N = 2 of the Higgs Abelian model and. the appearane of Bogomol'nyi equations[r]

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Conjectures on the normal covering number of finite symmetric and alternating groups

Conjectures on the normal covering number of finite symmetric and alternating groups

c can be taken as 0.025 for n > 792000. This settled the question as to whether γ(G) grows linearly in n, rather than growing more slowly as a constant times ϕ(n). Proof of the improved lower bound in [7] relies on certain number theoretic results (see [5]), and the value of c obtained is unrealistically small because of the many approximations needed first to obtain and next to apply those results. Thus, despite the innovative methods used to achieve the definitive result that γ(S n ) and γ(A n ) grow

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A surface with canonical map of degree 24

A surface with canonical map of degree 24

This research was partially supported by FCT (Portugal) under the project PTDC/MAT-GEO/0675/2012, the fellowship SFRH/BPD/111131/2015 and by CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds through the programs FEDER, under the part- nership agreement PT2020.

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The Influence of Small Amounts of Aluminium on the Spheroidization of Cast Iron with Cerium Mischmetal

The Influence of Small Amounts of Aluminium on the Spheroidization of Cast Iron with Cerium Mischmetal

The influence of aluminium (added in quantity from about 0.6% to about 2.8%) on both the alloy matrix and the shape of graphite precipitates in cast iron treated with a fixed amounts of cerium mischmetal (0.11%) and ferrosilicon (1.29%) is discussed in the paper. The metallographic examinations were carried out for specimens cut out of the separately cast rods of 20 mm diameter. It was found that the addition of aluminium in the amounts from about 0.6% to about 1.1% to the cast iron containing about 3% of carbon, about 3.7% of silicon (after graphitizing modification), and 0.1% of manganese leads to the occurrence of the ferrite-pearlite matrix containing cementite precipitates in the case of the treatment of the alloy with cerium mischmetal . The increase in the quantity of aluminium up to about 1.9% or up to about 2.8% results either in purely ferrite matrix in this first case or in ferrite matrix containing small amounts of pearlite in the latter one. Nodular graphite precipitates occurred only in cast iron containing 1.9% or 2.8% of aluminium, and the greater aluminium content resulted in the higher degree of graphite spheroidization. The noticeable amount of vermicular graphite precipitates accompanied the nodular graphite.
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On Invariant Rings of Sylow Subgroups of Finite Classical Groups

On Invariant Rings of Sylow Subgroups of Finite Classical Groups

Later a major motivation arose from the natural sciences, in particular physics, where certain configurations are expressed geometrically in terms of numerical functions and coordinates, which may depend on chosen viewpoints and coordinate systems. The change of coordinate systems can then be described by a transformation group, acting on those functions, and the “true, objective” physical entities turn out to be symmetry classes or “orbits” of those functions under the action of the transformation group.

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Variance component estimates applying random regression models for test-day milk yield in Caracu heifers ( Bos taurus Artiodactyla, Bovidae)

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers ( Bos taurus Artiodactyla, Bovidae)

Heritability estimates obtained with the two RRM (4,6,vf6 and 6,6,vf6) and by univariate analysis are pre- sented in Figure 3. The heritability estimates obtained with the TDMO ranged from 0.09 (12 th week) to 0.32 (42 nd week), with higher estimates at the end of lactation, proba- bly due to the lower number of records at these points. Heritabilities estimated by the 6,6,vf6 model ranged from 0.09 to 0.26, while those estimated by the 4,6,vf6 model ranged from 0.09 to 0.21. For both RRM, the estimates were lower during mid-lactation, from 14 th to 30 th week. In general, RRM heritability estimates were similar to those obtained by TDMO, with larger differences in test day milk yields around 14 th to 28 th weeks. The estimates obtained by 6,6,vf6 model oscillated more than those from 4,6,vf6 model, with higher heritabilities observed at the extremes of lactation. Trends of the heritability estimates, obtained by RRM, followed those reported in the literature, i.e., higher estimates at the beginning and towards the end of lactation (Strabel and Misztal, 1999; Tijani et al., 1999; Brotherstone et al., 2000). Difficulties to model the vari- ances at the extremes of lactation can be explained, in part, by the biological processes that occur at the beginning of lactation and the smaller number of records at the end. For Zebu and tropical native breeds, both reasons can be even more important. In general, these animals have not been as intensively selected for milk production as Holsteins and population sizes are smaller. It is usually necessary to keep the calf with the dam during milking and short lactations are frequent.
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On the groups satisfying the converse of Schur's theorem

On the groups satisfying the converse of Schur's theorem

by some authors. Recently, Podoski and Szegedy proved the truth of the converse of Schur’s theorem for capable groups. They also established an explicit bound for the index of the center of such groups. This paper is devoted to determine some families of groups among non-capable groups which satisfy the converse of Schur’s theorem and at the same time admit the Podoski and Szegedy’s bound as the upper bound for the index of their centers.

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Effects of eating disorders on oral fungal diversity

Effects of eating disorders on oral fungal diversity

The prevalence of eating disorders (EDs) has increased significantly over the years, mainly stimulated by a modern society that upholds thinness as a symbol of success and beauty. 1 Anorexia nervosa (AN) is charac- terized by weight loss at the expense of an extremely restricted diet, an unbridled quest for thinness, a dis- torted body image, and menstrual cycle alterations. Bulimia nervosa (BN) is characterized by binge-eating (quickly eating large quantities of food with little or no pleasure) alternating with behaviors to prevent weight gain. 1,2 Although classified separately in the Diagnostic and Statistical Manual edition IV (DSM-IV), 3 these 2 disorders are closely related because they have a com- mon psychopathology: excessive concern about weight and body shape (morbid fear of fatness). 4 EDs are accompanied by various clinical complications related to impaired nutritional status and unhealthy compensa- tion practices for weight control, such as induced vom-
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