A question on partial CAP-subgroups of finite groups

This paper has been published in Science China Mathematics, 55(5):961-966 (2012). Copyright 2012 by Science China Press and Springer-Verlag. The final publication is available at www.springerlink.com. http://link.springer.com/article/10.1007/s11425-011-4356-9 http://dx.doi.org/10.1007/s11425-011-4356-9A subgroup H of a finite group G is a partial CAP-subgroup of G if there is a chief series of G such that H either covers or avoids every chief factor of the series. The structural impact of the partial cover and avoidance property of some distinguished subgroups of a group has been studied by many authors. However there are still some open questions which deserve an answer. The purpose of the present paper is to give a complete answer to one of these questions.This work was supported by MEC of Spain, FEDER of European Union (Grant No. MTM-2007-68010-C03-02), MICINN of Spain (Grant No. MTM-2010-19938-C03-01), National Natural Science Foundation of China (Grant No. 11171353/A010201) and Natural Science Fund of Guangdong (Grant No. S2011010004447). Part of this research was carried out during a visit of the third author to the Departament d'Algebra, Universitat de Valencia, Burjassot, Valencia, Spain, and the Institut Universitari de Matematica Pura i Aplicada, Universitat Politecnica de Valencia, Valencia, Spain, between September, 2009 and August, 2010. He is grateful to both institutions for their warm hospitality and, in particular, to the Universitat Politecnica de Valencia for the financial support given via its Programme of Support to Research and Development 2010.http://link.springer.com/article/10.1007/s11425-011-4356-9Ballester Bolinches, A.; Esteban Romero, R.; Li, Y. (2012). A question on partial CAP-subgroups of finite groups. Science China Mathematics. 5(55). doi:10.1007/s11425-011-4356-9S555Ballester-Bolinches A, Ezquerro L M. Classes of Finite Groups. In: Mathematics and its Applications, vol. 584. New York: Springer, 2006Ballester-Bolinches A, Ezquerro L M, Skiba A N. Local embeddings of some families of subgroups of finite group. Acta Math Sin Engl Ser, 2009, 25: 869–882Ballester-Bolinches A, Ezquerro L M, Skiba A N. On second maximal subgroups of Sylow subgroups of finite groups. J Pure Appl Algebra, 2011, 215: 705–714Doerk K, Hawkes T. Finite Soluble Groups. In: De Gruyter Expositions in Mathematics, vol. 4. Berlin-New York: Walter de Gruyter, 1992Ezquerro L M. A contribution to the theory of finite supersolvable groups. Rend Sem Mat Univ Padova, 1993, 89: 161–170Fan Y, Guo X Y, Shum K P. Remarks on two generalizations of normality of subgroups (in Chinese). Chinese Ann Math Ser A, 2006, 27: 169–176Guo X Y, Wang L L. On finite groups with some semi cover-avoiding subgroups. Acta Math Sin Engl Ser, 2007, 23: 1689–1696Huppert B. Endliche Gruppen I. In: Grund Math Wiss, vol. 134. Berlin-Heidelberg-New York: Springer-Verlag, 1967Huppert B, Blackburn N. Finite Groups III. In: Grund Math Wiss, vol. 243. Berlin: Springer-Verlag, 1982Li Y M. On cover-avoiding subgroups of Sylow subgroups of finite groups. Rend Sem Mat Univ Padova, 2010, 123: 249–258Li Y M, Miao L, Wang Y M. On semi cover-avoiding maximal subgroups of Sylow subgroups of finite groups. Comm Algebra, 2009, 37: 1160–116

Theoretical study of the HS (v',,j' = 1) + O2;(v''=0,j''=1) reaction

We report a theoretical study of the title four-atom reaction for a wide range of translational energies, considering the reactants in the ground vibrational state and also in some vibrationally excited levels of the HS radical. All calculations have employed the quasi-classical trajectory (QCT) method and a reported double many-body expansion potential energy surface for ground electronic state of HSO2. Cross sections as well as specific rate constants for HS elimination are reported and compared with literature data for such processes. To account the zero-point energy problem in QCT calculations, an internal energy quantum mechanics threshold (IEQMT) criteria is used. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 200

The resonant damping of fast magnetohydrodynamic oscillations in a system of two coronal slabs

Observations of transversal coronal loop oscillations very often show the excitation and damping of oscillations in groups of coronal loops rather than in individual and isolated structures. We present results on the oscillatory properties (periods, damping rates, and spatial distribution of perturbations) for resonantly damped oscillations in a system of two inhomogeneous coronal slabs and compare them to the properties found in single slab loop models. A system of two identical coronal loops is modeled, in Cartesian geometry, as being composed by two density enhancements. The linear magnetohydrodynamic (MHD) wave equations for oblique propagation of waves are solved and the damping of the different solutions, due to the transversal inhomogeneity of the density profile, is computed. The physics of the obtained results is analyzed by an examination of the perturbed physical variables. We find that, due to the interaction between the loops, the normal modes of oscillation present in a single slab split into symmetric and antisymmetric oscillations when a system of two identical slabs is considered. The frequencies of these solutions may differ from the single slab results when the distance between the loops is of the order of a few slab widths. Oblique propagation of waves weakens this interaction, since solutions become more confined to the edges of the slabs. The damping is strong for surface-like oscillations, while sausage body-like solutions are unaffected. For some solutions, and small slab separations, the damping in a system of two loops differs substantially from the damping of a single loop.Comment: 25 pages, 9 figure

Long-range surface plasmon polariton excitation at the quantum level

We provide the quantum mechanical description of the excitation of long-range surface plasmon polaritons (LRSPPs) on thin metallic strips. The excitation process consists of an attenuated-reflection setup, where efficient photon-to-LRSPP wavepacket-transfer is shown to be achievable. For calculating the coupling, we derive the first quantization of LRSPPs in the polaritonic regime. We study quantum statistics during propagation and characterize the performance of photon-to-LRSPP quantum state transfer for single-photons, photon-number states and photonic coherent superposition states.Comment: 9 pages, 6 figures, RevTeX4; Accepted versio

A note on a result of Guo and Isaacs about p-supersolubility of finite groups

In this note, global information about a finite group is obtained by assuming that certain subgroups of some given order are S-semipermutable. Recall that a subgroup H of a finite group G is said to be S-semipermutable if H permutes with all Sylow subgroups of G of order coprime to |H|. We prove that for a fixed prime p, a given Sylow p-subgroup P of a finite group G, and a power d of p dividing |G| such that 1≤dd . This extends the main result of Guo and Isaacs in (Arch. Math. 105:215-222 2015). We derive some theorems that extend some known results concerning S-semipermutable subgroups

Ultrafast Quantum Gates in Circuit QED

We present a method of implementing ultrafast two-qubit gates valid for the ultrastrong coupling (USC) and deep strong coupling (DSC) regimes of light-matter interaction, considering state-of-the-art circuit quantum electrodynamics (QED) technology. Our proposal includes a suitable qubit architecture and is based on a four-step sequential displacement of an intracavity mode, operating at a time proportional to the inverse of the resonator frequency. Through ab initio calculations, we show that these quantum gates can be performed at subnanosecond time scales, while keeping the fidelity above 99%.Comment: 4 pages, 2 figures. Updated version to be published in Physical Review Letter

On certain products of permutable subgroups

[EN] In this paper, we study the structure of finite groups G = AB which are a weakly mutually sn-permutable product of the subgroups A and B, that is, A permutes with every subnormal subgroup of B containing A boolean AND B and B permutes with every subnormal subgroup of A containing A boolean AND B. We obtain generalisations of known results on mutually sn-permutable products.The first and fourth authors have been supported by the research grant PGC2018- 095140-B-I00 from the Ministerio de Ciencia, Innovación y Universidades and the Agencia Estatal de Investigación (Spanish Government) and FEDER (European Union), and PROMETEO/2017/057 from Generalitat (Valencian Community, Spain).Ballester-Bolinches, A.; Madanha, SY.; Mudziiri Shumba, TM.; Pedraza Aguilera, MC. (2022). On certain products of permutable subgroups. Bulletin of the Australian Mathematical Society. 105(2):278-285. https://doi.org/10.1017/S0004972721000617278285105

Damping mechanisms for oscillations in solar prominences

Small amplitude oscillations are a commonly observed feature in prominences/filaments. These oscillations appear to be of local nature, are associated to the fine structure of prominence plasmas, and simultaneous flows and counterflows are also present. The existing observational evidence reveals that small amplitude oscillations, after excited, are damped in short spatial and temporal scales by some as yet not well determined physical mechanism(s). Commonly, these oscillations have been interpreted in terms of linear magnetohydrodynamic (MHD) waves, and this paper reviews the theoretical damping mechanisms that have been recently put forward in order to explain the observed attenuation scales. These mechanisms include thermal effects, through non-adiabatic processes, mass flows, resonant damping in non-uniform media, and partial ionization effects. The relevance of each mechanism is assessed by comparing the spatial and time scales produced by each of them with those obtained from observations. Also, the application of the latest theoretical results to perform prominence seismology is discussed, aiming to determine physical parameters in prominence plasmas that are difficult to measure by direct means.Comment: 36 pages, 16 figures, Space Science Reviews (accepted

Z-permutable subgroups of finite groups

Let ℨ be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ℨ-permutable if H permutes with all members of ℨ. The main goal of this paper is to study the embedding of the ℨ-permutable subgroups and the influence of ℨ-permutability on the group structure

New insight into the SSC8 genetic determination of fatty acid composition in pigs

[EN] Background:Fat content and fatty acid composition in swine are becoming increasingly studied because of their effect on sensory and nutritional quality of meat. A QTL (quantitative trait locus) for fatty acid composition in backfat was previously detected on porcine chromosome 8 (SSC8) in an Iberian x Landrace F-2 intercross. More recently, a genome-wide association study detected the same genomic region for muscle fatty acid composition in an Iberian x Landrace backcross population. ELOVL6, a strong positional candidate gene for this QTL, contains a polymorphism in its promoter region (ELOVL6:c.-533C < T), which is associated with percentage of palmitic and palmitoleic acids in muscle and adipose tissues. Here, a combination of single-marker association and the haplotype-based approach was used to analyze backfat fatty acid composition in 470 animals of an Iberian x Landrace F2 intercross genotyped with 144 SNPs (single nucleotide polymorphisms) distributed along SSC8. Results:Two trait-associated SNP regions were identified at 93 Mb and 119 Mb on SSC8. The strongest statistical signals of both regions were observed for palmitoleic acid (C16:1(n-7)) content and C18:0/C16:0 and C18:1(n-7)/C16:1 (n-7) elongation ratios. MAML3 and SETD7 are positional candidate genes in the 93 Mb region and two novel microsatellites in MAML3 and nine SNPs in SETD7 were identified. No significant association for the MAML3 microsatellite genotypes was detected. The SETD7:c. 700G > T SNP, although statistically significant, was not the strongest signal in this region. In addition, the expression of MAML3 and SETD7 in liver and adipose tissue varied among animals, but no association was detected with the polymorphisms in these genes. In the 119 Mb region, the ELOVL6:c.-533C > T polymorphism showed a strong association with percentage of palmitic and palmitoleic fatty acids and elongation ratios in backfat. Conclusions:Our results suggest that the polymorphisms studied in MAML3 and SETD7 are not the causal mutations for the QTL in the 93 Mb region. However, the results for ELOVL6 support the hypothesis that the ELOVL6:c.-533C > T polymorphism has a pleiotropic effect on backfat and intramuscular fatty acid composition and that it has a role in the determination of the QTL in the 119 Mb region.This work was funded by MICINN AGL2008-04818-C03/GAN and MINECO AGL2011-29821-C02 and the Innovation Programme Consolider-Ingenio 2010 (CSD2007-00036). M. Revilla is a Master's student of Animal Breeding and Biotechnology of Reproduction (Polytechnical University of Valencia and Autonomous University of Barcelona). Y. Ramayo-Caldas was funded by a FPU grant (AP2008-01450), J. Corominas by a FPI scholarship from the Ministry of Education (BES-2009-018223) and A. Puig-Oliveras by a PIF scholarship (458-01-1/2011). 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Covalent Histone Modifications Underlie the Developmental Regulation of Insulin Gene Transcription in Pancreatic β Cells. Journal of Biological Chemistry, 278(26), 23617-23623. doi:10.1074/jbc.m303423200Ramayo-Caldas, Y., Mach, N., Esteve-Codina, A., Corominas, J., Castelló, A., Ballester, M., … Folch, J. M. (2012). Liver transcriptome profile in pigs with extreme phenotypes of intramuscular fatty acid composition. BMC Genomics, 13(1), 547. doi:10.1186/1471-2164-13-547Corominas, J., Ramayo-Caldas, Y., Puig-Oliveras, A., Pérez-Montarelo, D., Noguera, J. L., Folch, J. M., & Ballester, M. (2013). Polymorphism in the ELOVL6 Gene Is Associated with a Major QTL Effect on Fatty Acid Composition in Pigs. PLoS ONE, 8(1), e53687. doi:10.1371/journal.pone.005368