Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

On spectra of abelian group rings

In this paper we study the spectrum of integral group rings of finitely generated abelian groups G from the scheme-theoretic viewpoint. We prove that the (closed) singular points of Spec Z[G], the (closed) intersection points of the irreducible components of Spec Z[G] and the (closed) points over the prime divisors of vertical bar t(G)vertical bar coincide. We also determine the formal completion of Spec Z[G] at a singular point.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

On automorphisms of finite abelian p-groups

Let A be a finitely generated abelian group. We describe the automorphism group Aut(A) using the rank of A and its torsion part p-part A(p). For a finite abelian p-group A of type (k(1),..., k(n)), simple necessary and sufficient conditions for an n x n-matrix over integers to be associated with an automorphism of A are presented. Then, the automorphism group Aut(A) for a finite p-group A of type (k(1), k(2)) is analyzed. (C) 2008 Mathematical Institute Slovak Academy of Sciences.

Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

Fatigue and workability in Brazilian textile companies in different corporate social responsibility score groups

The aim of this study was to evaluate working conditions in the textile industry for different stages of Corporate Social Responsibility (CSR) development, and workers` perception of fatigue and workability. A cross-sectional study was undertaken with 126 workers in the production areas of five Brazilian textile plants. The corporate executive officers and managers of each company provided their personal evaluations of CSR. Companies were divided into 2 groups (higher and lower) of CSR scores. Workers completed questionnaires on fatigue, workability and working conditions. Ergonomic job analysis showed similar results for working conditions, independent of their CSR score. Multivariate analysis models were developed for fatigue and workability, indicating that they are both associated to factors related to working conditions and individual workers` characteristics and life styles. Work organization, (what, how, when, where and for how long the work is done), is also an associated factor for fatigue. This study suggests that workers` opinions should be taken into greater consideration when companies develop their CSR programs, in particular for those relating to working conditions. Relevance to industry: This paper underlines the importance of considering working conditions and workers` opinions of them, work organization and individual workers` characteristics and life styles in order to restore or to maintain workability and to reduce fatigue, independently of how developed a company may be in the field of Corporate Social Responsibility. (C) 2010 Elsevier B.V. All rights reserved.

Intragroup diffuse light in compact groups of galaxies - II. HCG 15, 35 and 51

This continuing study of intragroup light in compact groups of galaxies aims to establish new constraints to models of formation and evolution of galaxy groups, specially of compact groups, which are a key part in the evolution of larger structures, such as clusters. In this paper we present three additional groups (HCG 15, 35 and 51) using deep wide-field B- and R-band images observed with the LAICA camera at the 3.5-m telescope at the Calar Alto observatory (CAHA). This instrument provides us with very stable flat-fielding, a mandatory condition for reliably measuring intragroup diffuse light. The images were analysed with the OV_WAV package, a wavelet technique that allows us to uncover the intragroup component in an unprecedented way. We have detected that 19, 15 and 26 per cent of the total light of HCG 15, 35 and 51, respectively, are in the diffuse component, with colours that are compatible with old stellar populations and with mean surface brightness that can be its low as 28.4 B mag arcsec(-2). Dynamical masses, crossing times and mass-to-light ratios were recalculated using the new group parameters. Also tidal features were analysed using the wavelet technique.

The influence of halo assembly on galaxies and galaxy groups

In this paper, we study the variations of groups (galaxy properties according to the assembly history in Sloan Digital Sky Survey Data Release 6 (SDSS-DR6) selected groups. Using mock SDSS group catalogues, we find two suitable indicators of group formation time: (i) the isolation of the group, defined as the distance to the nearest neighbour ill terms of its virial radius and 00 the concentration. measured as the groups inner density calculated using the fifth nearest bright galaxy to the groups centre. Groups Within narrow ranges of Mass ill the mock catalO-Lie show increasing Ifl-OLIP alle With isolation and concentration. However, in the observational data the stellar age, as indicated by the spectral type, only shows a correlation with concentration. We study groups of similar mass and different assembly history. finding important differences ill their galaxy population. Particularly, ill high-mass SDSS groups. the number of members. mass-to-light ratios, red galaxy fractions and the magnitude difference between the brightest and second-brightest group galaxies, show different trends as a function of isolation and concentration, even when it is expected that the latter two quantities correlate with group age. Conversely. low-mass SDSS groups appear to be less sensitive to their assembly history. The correlations detected in the SDSS are not consistent with the trends measured in the mock catalogues. However, discrepancies can he explained in terms of the disagreement found in the a-e-isolation trends, suggesting that the model might be overestimating the effects of, environment, We discuss how the modelling of the cold gas ill satellite galaxies could be responsible for this problem. These results call be Used to improve our Understanding of the evolution of galaxies ill high-density environments.

Segregation effects according to the evolutionary stage of galaxy groups

We study segregation phenomena in 57 groups selected from the 2dF Percolation-Inferred Galaxy Groups (2PIGG) catalogue of galaxy groups. The sample corresponds to those systems located in areas of at least 80 per cent redshift coverage out to 10 times the radius of the groups. The dynamical state of the galaxy systems was determined after studying their velocity distributions. We have used the Anderson-Darling test to distinguish relaxed and non-relaxed systems. This analysis indicates that 84 per cent of groups have galaxy velocities consistent with the normal distribution, while 16 per cent of them have more complex underlying distributions. Properties of the member galaxies are investigated taking into account this classification. Our results indicate that galaxies in Gaussian groups are significantly more evolved than galaxies in non-relaxed systems out to distances of similar to 4R(200), presenting significantly redder (B - R) colours. We also find evidence that galaxies with M(R) <= -21.5 in Gaussian groups are closer to the condition of energy equipartition.

Homotopy type of gauge groups of quaternionic line bundles over spheres

Let P be a principal S(3)-bundle over a sphere S(n), with n >= 4. Let G(p) be the gauge group of P. The homotopy type of G(p) when n - 4 was studied by A. Kono in [A. Kono, A note on the homotopy type of certain gauge groups, Proc. Roy. Soc. Edinburgh Sect. A 117 (1991) 295-297]. In this paper we extend his result anti we study the homotopy type of the gauge group of these bundles for all n <= 25. (C) 2008 Elsevier B.V. All rights reserved.

Topological interactions in warped extra dimensions

Topological interactions will be generated in theories with compact extra dimensions where fermionic chiral zero modes have different localizations. This is the case in many warped extra dimension models where the right-handed top quark is typically localized away from the left-handed one. Using deconstruction techniques, we study the topological interactions in these models. These interactions appear as trilinear and quadrilinear gauge boson couplings in low energy effective theories with three or more sites, as well as in the continuum limit. We derive the form of these interactions for various cases, including examples of Abelian, non-Abelian and product gauge groups of phenomenological interest. The topological interactions provide a window into the more fundamental aspects of these theories and could result in unique signatures at the Large Hadron Collider, some of which we explore.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

The game of contacts: Estimating the social visibility of groups

Estimating the sizes of hard-to-count populations is a challenging and important problem that occurs frequently in social science, public health, and public policy. This problem is particularly pressing in HIV/AIDS research because estimates of the sizes of the most at-risk populations-illicit drug users, men who have sex with men, and sex workers-are needed for designing, evaluating, and funding programs to curb the spread of the disease. A promising new approach in this area is the network scale-up method, which uses information about the personal networks of respondents to make population size estimates. However, if the target population has low social visibility, as is likely to be the case in HIV/AIDS research, scale-up estimates will be too low. In this paper we develop a game-like activity that we call the game of contacts in order to estimate the social visibility of groups, and report results from a study of heavy drug users in Curitiba, Brazil (n = 294). The game produced estimates of social visibility that were consistent with qualitative expectations but of surprising magnitude. Further, a number of checks suggest that the data are high-quality. While motivated by the specific problem of population size estimation, our method could be used by researchers more broadly and adds to long-standing efforts to combine the richness of social network analysis with the power and scale of sample surveys. (C) 2010 Elsevier B.V. All rights reserved.