Groups in which every subgroup is modular-by-finite

A group G is called a BCF-group if there is a positive integer κ such that |X : XG| ≤ κ for each subgroup X of G. The structure of BCF-groups has been studied by Buckley, Lennox, Neumann, Smith and Wiegold; they proved in particular that locally finite groups with the property BCF are Abelian-by-finite. As a group lattice version of this concept, we say that a group G is a BMF-group if there is a positive integer κ such that every subgroup X of G contains a modular subgroup Y of G for which the index |X : Y| is finite and the number of its prime divisors with multiplicity is bounded by κ (it is known that that such number can be characterised by purely lattice-theoretic considerations, and so it is invariant under lattice isomorphisms of groups). It is proved here that any locally finite BMF-group contains a subgroup of finite index with modular subgroup lattice

On a new theoretical framework for RR Lyrae stars I: the metallicity dependence

We present new nonlinear, time-dependent convective hydrodynamical models of RR Lyrae stars computed assuming a constant helium-to-metal enrichment ratio and a broad range in metal abundances (Z=0.0001--0.02). The stellar masses and luminosities adopted to construct the pulsation models were fixed according to detailed central He burning Horizontal Branch evolutionary models. The pulsation models cover a broad range in stellar luminosity and effective temperatures and the modal stability is investigated for both fundamental and first overtones. We predict the topology of the instability strip as a function of the metal content and new analytical relations for the edges of the instability strip in the observational plane. Moreover, a new analytical relation to constrain the pulsation mass of double pulsators as a function of the period ratio and the metal content is provided. We derive new Period-Radius-Metallicity relations for fundamental and first-overtone pulsators. They agree quite well with similar empirical and theoretical relations in the literature. From the predicted bolometric light curves, transformed into optical (UBVRI) and near-infrared (JHK) bands, we compute the intensity-averaged mean magnitudes along the entire pulsation cycle and, in turn, new and homogenous metal-dependent (RIJHK) Period-Luminosity relations. Moreover, we compute new dual and triple band optical, optical--NIR and NIR Period-Wesenheit-Metallicity relations. Interestingly, we find that the optical Period-W(V,B-V) is independent of the metal content and that the accuracy of individual distances is a balance between the adopted diagnostics and the precision of photometric and spectroscopic datasets.Comment: 51 pages, 20 figures, 9 tables, accepted for publication on Ap

Variable stars and stellar populations in Andromeda XXI: II. Another merged galaxy satellite of M31?

B and V time-series photometry of the M31 dwarf spheroidal satellite Andromeda XXI (And XXI) was obtained with the Large Binocular Cameras at the Large Binocular Telescope. We have identified 50 variables in And XXI, of which 41 are RR Lyrae stars (37 fundamental-mode RRab, and 4 first-overtone RRc, pulsators) and 9 are Anomalous Cepheids (ACs). The average period of the RRab stars ( = 0.64 days) and the period-amplitude diagram place And~XXI in the class of Oosterhoff II - Oosterhoff-Intermediate objects. From the average luminosity of the RR Lyrae stars we derived the galaxy distance modulus of (m-M)$_0$=$24.40\pm0.17$ mag, which is smaller than previous literature estimates, although still consistent with them within 1 $\sigma$. The galaxy color-magnitude diagram shows evidence for the presence of three different stellar generations in And~XXI: 1) an old ($\sim$ 12 Gyr) and metal poor ([Fe/H]=$-$1.7 dex) component traced by the RR Lyrae stars; 2) a slightly younger (10-6 Gyr) and more metal rich ([Fe/H]=$-$1.5 dex) component populating the red horizontal branch, and 3) a young age ($\sim$ 1 Gyr) component with same metallicity, that produced the ACs. Finally, we provide hints that And~XXI could be the result of a minor merging event between two dwarf galaxies.Comment: accepted for publications in Ap

Theoretical models for classical Cepheids. VIII. Effects of helium and heavy elements abundance on the Cepheid distance scale

Previous nonlinear fundamental pulsation models for classical Cepheids with metal content Z <= 0.02 are implemented with new computations at super-solar metallicity (Z=0.03, 0.04) and selected choices of the helium-to-metal enrichment ratio DeltaY/Delta Z. On this basis, we show that the location into the HR diagram of the Cepheid instability strip is dependent on both metal and helium abundance, moving towards higher effective temperatures with decreasing the metal content (at fixed Y) or with increasing the helium content (at fixed Z). The contributions of helium and metals to the predicted Period-Luminosity and Period-Luminosity-Color relations are discussed, as well as the implications on the Cepheid distance scale. Based on these new results, we finally show that the empirical metallicity correction suggested by Cepheid observations in two fields of the galaxy M101 may be accounted for, provided that the adopted helium-to-metal enrichment ratio is reasonably high (Delta Y/Delta Z ~ 3.5).Comment: 23 pages, including 6 postscript figures, accepted for publication on Ap

Groups with many abelian subgroups

AbstractIt is known that a (generalized) soluble group whose proper subgroups are abelian is either abelian or finite, and finite minimal non-abelian groups are classified. Here we describe the structure of groups in which every subgroup of infinite index is abelian

Preserved Extra-Foveal Processing of Object Semantics in Alzheimer’s Disease

Alzheimer’s disease (AD) patients underperform on a range of tasks requiring semantic processing, but it is unclear whether this impairment is due to a generalised loss of semantic knowledge or to issues in accessing and selecting such information from memory. The objective of this eye-tracking visual search study was to determine whether semantic expectancy mechanisms known to support object recognition in healthy adults are preserved in AD patients. Furthermore, as AD patients are often reported to be impaired in accessing information in extra-foveal vision, we investigated whether that was also the case in our study. Twenty AD patients and 20 age-matched controls searched for a target object among an array of distractors presented extra-foveally. The distractors were either semantically related or unrelated to the target (e.g., a car in an array with other vehicles or kitchen items). Results showed that semantically related objects were detected with more difficulty than semantically unrelated objects by both groups, but more markedly by the AD group. Participants looked earlier and for longer at the critical objects when these were semantically unrelated to the distractors. Our findings show that AD patients can process the semantics of objects and access it in extra-foveal vision. This suggests that their impairments in semantic processing may reflect difficulties in accessing semantic information rather than a generalised loss of semantic memory

Impact of Rubin Observatory LSST Template Acquisition Strategies on Early Science from the Transients and Variable Stars Science Collaboration: Non-time-critical Science Cases

Vera C. Rubin Observatory Legacy Survey of Space and Time, LSST, will revolutionize modern astronomy by producing an extremely deep (coadded depth ~27 mag) depth-limited survey of the entire southern sky (LSST Science Collaboration et al. 2009). The 8.4 m large-aperture, wide-field telescope, which is based in Cerro Pachón, will image the entire Southern sky every three nights in multiple bands (SDSS-u, g, r, i, z, y) and produce a fire-hose of data, 20 Tb each night, concluding in a 60 petabyte data set as the legacy of the 10 yr survey. Extracting meaningful light curves from variable objects requires difference imaging to both identify variability and calibrate light curve data products. Templates, co-added groups of visits that act as an image of the "static" sky, are a key component of Difference Imaging Analysis (DIA) and as such are of paramount importance for all science that involves variable objects. As the "non-time-critical" science cases discussed here are mostly periodic, they generally do not depend upon the survey alert stream; however, templates are still crucial for performing science and calibrations during the first year. We provide recommendations for observing strategies for template acquisition starting from commissioning and through Year 1 of the survey

The Carina Project IX: on Hydrogen and helium burning variables

We present new multi-band (UBVI) time-series data of helium burning variables in the Carina dwarf spheroidal galaxy. The current sample includes 92 RR Lyrae-six of them are new identifications-and 20 Anomalous Cepheids, one of which is new identification. The analysis of the Bailey diagram shows that the luminosity amplitude of the first overtone component in double-mode variables is located along the long-period tail of regular first overtone variables, while the fundamental component is located along the short-period tale of regular fundamental variables. This evidence further supports the transitional nature of these objects. Moreover, the distribution of Carina double-mode variables in the Petersen diagram (P_1/P_0 vs P_0) is similar to metal-poor globulars (M15, M68), to the dwarf spheroidal Draco and to the Galactic Halo. This suggests that the Carina old stellar population is metal-poor and affected by a small spread in metallicity. We use trigonometric parallaxes for five field RR Lyrae stars to provide an independent estimate of the Carina distance using the observed reddening free Period--Wesenheit [PW, (BV)] relation. Theory and observations indicate that this diagnostic is independent of metallicity. We found a true distance modulus of \mu=20.01\pm0.02 (standard error of the mean) \pm0.05 (standard deviation) mag. We also provided independent estimates of the Carina true distance modulus using four predicted PW relations (BV, BI, VI, BVI) and we found: \mu=(20.08\pm0.007\pm0.07) mag, \mu=(20.06\pm0.006\pm0.06) mag, \mu=(20.07\pm0.008\pm0.08) mag and \mu=(20.06\pm0.006\pm0.06) mag. Finally, we identified more than 100 new SX Phoenicis stars that together with those already known in the literature (340) make Carina a fundamental laboratory to constrain the evolutionary and pulsation properties of these transitional variables.Comment: 44 pages, 13 tables, 13 figures, Accepted for publication in Ap