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

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

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

On the product of two π-decomposable soluble groups

Let the group G = AB be a product of two π-decomposable sub-groups A = Oπ(A) × Oπ' (A) and B = Oπ(B) × Oπ' (B) where π is a set of primes. The authors conjecture that Oπ(A)Oπ(B) = Oπ(B)Oπ(A) if π is a set of odd primes. In this paper it is proved that the conjecture is true if A and B are soluble. A similar result with certain additional restrictions holds in the case 2 ∈ π. Moreover, it is shown that the conjecture holds if Oπ '(A) and Oπ'(B) have coprime orders

Kinematic and kinetic patterns related to free-walking in parkinson’s disease

The aim of this study is to compare the properties of free-walking at a natural pace between mild Parkinson’s disease (PD) patients during the ON-clinical status and two control groups. In-shoe pressure-sensitive insoles were used to quantify the temporal and force characteristics of a 5-min free-walking in 11 PD patients, in 16 young healthy controls, and in 12 age-matched healthy controls. Inferential statistics analyses were performed on the kinematic and kinetic parameters to compare groups’ performances, whereas feature selection analyses and automatic classification were used to identify the signature of parkinsonian gait and to assess the performance of group classification, respectively. Compared to healthy subjects, the PD patients’ gait pattern presented significant differences in kinematic parameters associated with bilateral coordination but not in kinetics. Specifically, patients showed an increased variability in double support time, greater gait asymmetry and phase deviation, and also poorer phase coordination. Feature selection analyses based on the ReliefF algorithm on the differential parameters in PD patients revealed an effect of the clinical status, especially true in double support time variability and gait asymmetry. Automatic classification of PD patients, young and senior subjects confirmed that kinematic predictors produced a slightly better classification performance than kinetic predictors. Overall, classification accuracy of groups with a linear discriminant model which included the whole set of features (i.e., demographics and parameters extracted from the sensors) was 64.1%

Finite trifactorized groups and pi-decomposability

The first author would like to thank the Universitat de Valencia for its warm hospitality and financial support during the preparation of this paper.Kazarin, LS.; Martínez-Pastor, A.; Perez Ramos, MD. (2018). Finite trifactorized groups and pi-decomposability. Bulletin of the Australian Mathematical Society. 97(2):218-228. https://doi.org/10.1017/S0004972717001034S21822897

The lightest flavor--singlet qqq baryons as witnesses to color

We present a new computation in a field-theoretical model of Coulomb gauge QCD of the first radial and angular excitations of a qqq system in a SU(3) flavor singlet state, Lambda_S. The traditional motivation for the study is that the absence of flavor singlets in the lowest-lying spectrum is a direct consequence of the color degree of freedom. (The calculation is tested with decuplet baryons Delta(1232) and Omega(1672).) We also analyze decay branching fractions of the flavor singlet baryon for various masses with the simplest effective Lagrangians