Square-free class sizes in products of groups

We obtain some structural properties of a factorised group $G = AB$, given that the conjugacy class sizes of certain elements in $A\cup B$ are not divisible by $p^2$, for some prime $p$. The case when $G = AB$ is a mutually permutable product is especially considered

InAs/InP single quantum wire formation and emission at 1.5 microns

Isolated InAs/InP self-assembled quantum wires have been grown using in situ accumulated stress measurements to adjust the optimal InAs thickness. Atomic force microscopy imaging shows highly asymmetric nanostructures with average length exceeding more than ten times their width. High resolution optical investigation of as-grown samples reveals strong photoluminescence from individual quantum wires at 1.5 microns. Additional sharp features are related to monolayer fluctuations of the two dimensional InAs layer present during the early stages of the quantum wire self-assembling process.Comment: 4 pages and 3 figures submitted to Applied Physics Letter

Magnetic topology of the north solar pole

We study the polar magnetism near an activity maximum when these regions change their polarity, from which it is expected that its magnetism should be less affected by the global field. To fully characterise the magnetic field vector, we use deep full Stokes polarimetric observations of the 15648.5 {\AA} and 15652.8 {\AA} FeI lines. We observe the north pole as well as a quiet region at disc centre to compare their field distributions. In order to calibrate the projection effects, we observe an additional quiet region at the east limb. We find that the two limb datasets share similar magnetic field vector distributions. This means that close to a maximum, the poles look like typical limb, quiet-Sun regions. However, the magnetic field distributions at the limbs are different from the distribution inferred at disc centre. At the limbs, we infer a new population of magnetic fields with relatively strong intensities ($\sim$600-$\sim$800 G), inclined by 30 deg with respect to the line of sight, and with an azimuth aligned with the solar disc radial direction. We propose that this new population at the limbs is due to the observation of unresolved magnetic loops as seen close to the limb. These loops have typical granular sizes as measured in the disc centre. At the limbs, where the spatial resolution decreases, we observe them spatially unresolved, which explains the new population of magnetic fields that is inferred. This is the first (indirect) evidence of small-scale magnetic loops outside the disc centre and would imply that these small-scale structures are ubiquitous on the entire solar surface. This result has profound implications for the energetics not only of the photosphere, but also of the outer layers since these loops have been reported to reach the chromosphere and the low corona

Biscarboxy-Functionalized Imidazole and Palladium as Highly Active Catalytic System in Protic Solvents: Methanol and Water

The coupling reaction between aryl bromides and boron reagents is efficiently catalyzed by an in situ generated palladium complex obtained from palladium(II) acetate (0.1 mol%) and 1,3-bis(carboxymethyl)imidazole (0.2 mol%). The catalytic system is very active in protic solvents, especially in methanol. Biaryl derivatives have been prepared in good isolated yields (up to >99%), and additionally styrene and stilbene derivatives have also been prepared by means of this protocol.Financial support from the Ministerio de Ciencia e Innovación (MICINN) of Spain (Project Nos. CTQ2007-65218, CTQ2011-24165, Consolider Ingenio 2010 CSD2007-00006), the Generalitat Valenciana (PROMETEO/2009/039 and FEDER), and the Universidad de Alicante is acknowledged

The D-pi-property on products of pi-decomposable groups

[EN] The aim of this paper is to prove the following result: Let pi be a set of odd primes. If the group G = AB is the product of two p-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then G has a unique conjugacy class of Hall pi-subgroups, and any p-subgroup is contained in a Hall pi-subgroup (i.e. G satisfies property D-pi)Research supported by Proyectos PROMETEO/2017/057 from the Generalitat Valenciana (Valencian Community, Spain), and PGC2018-096872-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades, Spain, and FEDER, European Union; and second author also by Project VIP-008 of Yaroslavl P. Demidov State University.Kazarin, L.; Martínez-Pastor, A.; Pérez-Ramos, MD. (2020). The D-pi-property on products of pi-decomposable groups. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 115(1):1-18. https://doi.org/10.1007/s13398-020-00950-z118115

1,2-Functionalized Imidazoles as Palladium Ligands: An Efficient and Robust Catalytic System for the Fluorine-Free Hiyama Reaction

A variety of hydroxy- and amino-functionalized imidazoles were prepared from 1-methyl- and 1-(diethoxymethyl)imidazole by means of isoprene-mediated lithiation followed by reaction with an electrophile. These compounds in combination with palladium acetate were screened as catalyst systems for the Hiyama reaction under fluorine-free conditions using microwave irradiation. The systematic study of the catalytic system showed 1-methyl-2-aminoalkylimidazole derivative L1 to be the best ligand, which was employed under solvent-free conditions with a 1:2 Pd/ligand ratio and TBAB (20 mol-%) as additive. The study has revealed an interaction between the Pd/ligand ratio and the amount of TBAB. The established catalytic system presented a certain degree of robustness, and it has been successfully employed in the coupling of a range of aryl bromides and chlorides with different aryl siloxanes. Furthermore, both reagents were employed in an equimolecular amount, without an excess of organosilane.Financial support from the Spanish Ministerio de Ciencia e Innovación (MICINN) (project numbers CTQ2007-65218, CTQ2011-24165), from Consolider Ingenio 2010 (CSD2007-00006), from the Generalitat Valenciana (PROMETEO/2009/039), from the Fondos Europeos para el Desarrollo Regional (FEDER) and from the Universidad de Alicante is acknowledged

1,3-Bis(carboxymethyl)imidazolium Chloride as a Metal-Free and Recyclable Catalyst for the Synthesis of N-Allylanilines by Allylic Substitution of Alcohols

The 1,3-bis(carboxymethyl)imidazolium chloride, which is easily and in a straightforward manner prepared readily from starting materials in multigram scale, is employed as catalyst in the synthesis of N-allylanilines by allylic substitution of alcohols with anilines. This metal-free catalyst allows the reaction to be carried out under mild reaction conditions (80 °C and air open vessel) and proved to be efficient for a diversity of anilines and allylic alcohols, providing exclusively the product of N-substitution independently of the substituents in the aniline reactant. The process described is simple and effective, allowing N-allylanilines to be obtained in preparative scale [e.g., 3.30 g of N-(1,3-diphenylallyl)-4-nitroaniline]. The catalyst could be reused up to 15 cycles without loss of activity, proving its robustness.This work was financially supported by the University of Alicante (VIGROB-285) and the Spanish Ministerio de Economía y Competitividad (CTQ2015-66624-P). M.A.S. thanks the Spanish Ministerio de Educación, Cultura y Deporte for a predoctoral fellowship (FPU15/06040)