Products of pairwise totally permutable groups

[EN] In this paper finite groups factorized as products of pairwise totally permutable subgroups are studied in the framework of Fitting classesA.M.-P. and M.D.P.-R. were both supported by Proyecto BMF20001-1667-C03-03, Ministerio de Ciencia y Tecnolog´ıa and FEDER, Spain.Hauck, P.; Martínez Pastor, A.; Pérez-Ramos, M. (2003). Products of pairwise totally permutable groups. Proceedings of the Edinburgh Mathematical Society. 46(1):147-157. https://doi.org/10.1017/S0013091502000299S14715746

Nilpotent-like Fitting formations of finite soluble groups

[EN] In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.This research has been supported by Proyecto PB 97-0674-C02-02 of DGICYT, Ministerio de Educación y Ciencia, Spain.Ballester-Bolinches, A.; Pérez-Ramos, M.; Martínez Pastor, A. (2000). Nilpotent-like Fitting formations of finite soluble groups. Bulletin of the Australian Mathematical Society. 62(3):427-433. https://doi.org/10.1017/S0004972700018943S42743362

An analytic model for a cooperative ballistic deposition in one dimension

We formulate a model for a cooperative ballistic deposition (CBD) process whereby the incoming particles are correlated with the ones already adsorbed via attractive force. The strength of the correlation is controlled by a tunable parameter $a$ that interpolates the classical car parking problem at $a=0$, the ballistic deposition at $a=1$ and the CBD model at $a>1$. The effects of the correlation in the CBD model are as follows. The jamming coverage $q(a)$ increases with the strength of attraction $a$ due to an ever increasing tendency of cluster formation. The system almost reaches the closest packing structure as $a\to\infty$ but never forms a percolating cluster which is typical to 1D system. In the large $a$ regime, the mean cluster size $k$ increases as $a^{1/2}$. Furthermore, the asymptotic approach towards the closest packing is purely algebraic both with $a$ as $q(\infty)-q(a) \sim a^{-1/2}$ and with $k$ as $q(\infty)-q(k) \sim k^{-1}$ where $q(\infty)\simeq 1$.Comment: 9 pages (in Revtex4), 9 eps figures; Submitted to publicatio

Products of finite connected subgroups

For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if e L for all a e A and b e B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups

A family of dominant Fitting classes of finite soluble groups

[EN] In this paper a large family of dominant Fitting classes of finite soluble groups and the description of the corresponding injectors are obtained. Classical constructions of nilpotent and Lockett injectors as well as p-nilpotent injectors arise as particular cases.This research has been supported by Proyecto PB 94-0965 of DGICYT, Ministerio de Educacion y Ciencia of Spain.Ballester-Bolinches, A.; Martínez Pastor, A.; Pérez-Ramos, M. (1998). A family of dominant Fitting classes of finite soluble groups. Journal of the Australian Mathematical Society Series a-pure mathematics and statistics. 64(1):33-43. https://doi.org/10.1017/S1446788700001270S3343641[6] Lockett F. P. , On the theory of Fitting classes of finite soluble groups (Ph.D. thesis, University of Warwick, 1971).Ballester-Bolinches, A. (1992). A note on saturated formations. Archiv der Mathematik, 58(2), 110-113. doi:10.1007/bf01191873Ballester-Bolinches, A., Doerk, K., & Pérez-Ramos, M. . (1992). On the lattice of J-subnormal subgroups. Journal of Algebra, 148(1), 42-52. doi:10.1016/0021-8693(92)90235-eDoerk, K., & Hawkes, T. O. (1992). Finite Soluble Groups. doi:10.1515/9783110870138Ballester-Bolinches, A., Pedraza-Aguilera, M. C., & Pérez-Ramos, M. D. (1996). OnF-Subnormal Subgroups andF-Residuals of Finite Soluble Groups. Journal of Algebra, 186(1), 314-322. doi:10.1006/jabr.1996.0375Ballesterbolinches, A., & Perezramos, M. D. (1995). On F-Critical Groups. Journal of Algebra, 174(3), 948-958. doi:10.1006/jabr.1995.116

Application of Anodic Stripping Voltammetry to assess sorption performance of an industrial waste entrapped in alginate beads to remove As(V)

AbstractA solid waste material containing Fe(III) and other metal (hydr)oxides produced in a metal surface treatment industry has been investigated for As(V) removal. In order to facilitate sorbent application, 2% of raw material has been entrapped in calcium alginate gel matrix (2% O-CA).An accurate characterization of the sorption on gel beads was undertaken, considering thermodynamic and kinetic aspects. All experiments were carried out at pH 8, since the maximum As(V) sorption was reached between pH 6 and 9. About isotherms, the best fit was obtained considering the Langmuir model and a capacity of 1.9mg/g was achieved. The kinetic profiles evidenced that a quantitative sorption was obtained within 10h. The 2% O-CA beads were also tested for continuous As(V) removal in a fixed bed column. Experiments were performed at constant flow rate, and varying the inlet As(V) concentration. With a view to design an automatic system for As(V) analysis in the outlet flow, the suitability of applying Anodic Stripping Voltammetry was evaluated: the method resulted appropriated to follow the As(V) content in the outlet solutions of columns with metal inlet concentration <1 mg/L.These results suggested that 2% O-CA beads could be a promising sorbent candidate for As(V) removal

A reduction theorem for a conjecture on products of two ¿-decomposable groups

[EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All rights reserved.The second and third author have been supported by Proyecto MTM2010-19938-C03-02, Ministerio de Economia y Competitividad, Spain. The first author would like to thank the Universitat de Valencia and the Universitat Politecnica de Valencia for their warm hospitality during the preparation of this paper. He has been also supported by RFBR project 13-01-00469.Kazarin, LS.; Martínez Pastor, A.; Perez Ramos, MD. (2013). A reduction theorem for a conjecture on products of two ¿-decomposable groups. Journal of Algebra. 379:301-313. https://doi.org/10.1016/j.jalgebra.2013.01.017S30131337

Systemic Risk in a Unifying Framework for Cascading Processes on Networks

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.Comment: 43 pages, 16 multipart figure

Random Geometric Graphs

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bi-partitioning are included.Comment: 16 pages, 10 figures. Minor changes. Added reference

On finite products of groups and supersolubility

Two subgroups X and Y of a group G are said to be conditionally permutable in G if X permutes with Y(g) for some element g E G. i.e., XY(g) is a subgroup of G. Using this permutability property new criteria for the product of finite supersoluble groups to be supersoluble are obtained and previous results are recovered. Also the behaviour of the supersoluble residual in products of finite groups is studied.Research supported by Proyecto MTM2007-68010-C03-03, Ministerio de Educacion y Ciencia and FEDER, Spain.Arroyo Jordá, M.; Arroyo Jordá, P.; Martínez Pastor, A.; Perez-Ramos, M. (2010). On finite products of groups and supersolubility. Journal of Algebra. 323(10):2922-2934. https://doi.org/10.1016/j.jalgebra.2010.01.001S292229343231