Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut(G).

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

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.

On automorphisms of split metacyclic groups

Let D( m, n; k) be the semi-direct product of two finite cyclic groups Z/m = < x > and Z/n = < y >, where the action is given by yxy(-1) = x(k). In particular, this includes the dihedral groups D(2m). We calculate the automorphism group Aut (D(m, n; k)).

On cohomologies and extensions of cyclic groups

Cohomology groups H(s)(Z(n), Z(m)) are studied to describe all groups up to isomorphism which are (central) extensions of the cyclic group Z(n) by the Z(n)-module Z(m). Further, for each such a group the number of non-equivalent extensions is determined. (C) 2011 Elsevier B.V. All rights reserved.

A NOTE ON FREE GROUPS IN THE RING OF FRACTIONS OF SKEW POLYNOMIAL RINGS

Let L be a function field over the rationals and let D denote the skew field of fractions of L[t; sigma], the skew polynomial ring in t, over L, with automorphism sigma. We prove that the multiplicative group D(x) of D contains a free noncyclic subgroup.

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.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

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.

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.