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.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

ALTERNATING UNITS AS FREE FACTORS IN THE GROUP OF UNITS OF INTEGRAL GROUP RINGS

Let G be a group of odd order that contains a non-central element x whose order is either a prime p >= 5 or 3(l), with l >= 2. Then, in U(ZG), the group of units of ZG, we can find an alternating unit u based on x, and another unit v, which can be either a bicyclic or an alternating unit, such that for all sufficiently large integers m we have that < u(m), v(m)> = < u(m)> * < v(m)> congruent to Z * Z.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Involutions and free pairs of bicyclic units in integral group rings

If * : G -> G is an involution on the finite group G, then * extends to an involution on the integral group ring Z[G] . In this paper, we consider whether bicyclic units u is an element of Z[G] exist with the property that the group < u, u*> generated by u and u* is free on the two generators. If this occurs, we say that (u, u*)is a free bicyclic pair. It turns out that the existence of u depends strongly upon the structure of G and on the nature of the involution. One positive result here is that if G is a nonabelian group with all Sylow subgroups abelian, then for any involution *, Z[G] contains a free bicyclic pair.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Group identities on symmetric units

Let F be an infinite field of characteristic different from 2, G a group and * an involution of G extended by linearity to an involution of the group algebra FG. Here we completely characterize the torsion groups G for which the *-symmetric units of FG satisfy a group identity. When * is the classical involution induced from g -> g(-1), g is an element of G, this result was obtained in [ A. Giambruno, S. K. Sehgal, A. Valenti, Symmetric units and group identities, Manuscripta Math. 96 (1998) 443-461]. (C) 2009 Elsevier Inc. All rights reserved.

The core characteristics and nursing care activities in psychiatric intensive care units in Sweden

Internationally, research on psychiatric intensive care units (PICUs) commonly reportsresults from demographic studies such as criteria for admission, need for involuntary treatment, andthe occurrence of violent behaviour. A few international studies describe the caring aspect of thePICUs based specifically on caregivers’ experiences. The concept of PICU in Sweden is not clearlydefined. The aim of this study is to describe the core characteristics of a PICU in Sweden and todescribe the care activities provided for patients admitted to the PICUs. Critical incident techniquewas used as the research method. Eighteen caregivers at a PICU participated in the study bycompleting a semistructured questionnaire. In-depth interviews with three nurses and two assistantnurses also constitute the data. An analysis of the content identified four categories that characterizethe core of PICU: the dramatic admission, protests and refusal of treatment, escalating behaviours, andtemporarily coercive measure. Care activities for PICUs were also analysed and identified as controlling– establishing boundaries, protecting – warding off, supporting – giving intensive assistance, andstructuring the environment. Finally, the discussion put focus on determining the intensive aspect ofpsychiatric care which has not been done in a Swedish perspective before. PICUs were interpreted asa level of care as it is composed by limited structures and closeness in care.

Parent’s experiences of feeding their preterm infant in Neonatal Units in Sweden. : Ethnographic design

Introduction: Studies have shown that having a preterm infant may cause stress and powerlessness for parents. It is important to support parents around the feeding situation, and that the Neonatal Intensive Care Unit (NICU) has appropriate space and place to help the family to bond to each other. For the healthcare professionals it is important to promote skin-to-skin contact and breastfeeding; particularly for preterm infants. There are many studies on parent’s experiences of NICUs and a few studies on parent’s experiences of feeding their infant in the NICU. Objective: The objective of this study was to explore parents experiences of feeding their infant in the NICU. Design: The study was conducted using an ethnographic design. Results: A global theme of ‘The journey in feeding’ was developed from four organising themes: ‘Ways of infant feeding’; ‘Environmental influences’; ‘Relationships’ and ‘Emotional factors’. These themes illustrate the challenges mothers reported with different methods of feeding. The environment had a big impact on parent’s experiences of infant feeding. Some mothers felt that breastfeeding seemed unnatural because their infant was so tiny but breastfeeding and skin-to-skin contact helped them to bond to their infant. The mothers thought it was difficult to keep up with the milk production by only pumping. Routines were not inviting parents to find their own rhythm. They also felt stressed about the weighing. Healthcare professionals had positive and negative influences on the parents. Conclusions: This study demonstrates that while all parents expressed the wish to breastfeed, their ‘journey in feeding’ was highly influenced by method of feeding, environmental, relational and emotional factors. The general focus upon routines and assessing milk intake generated anxiety and reduced relationality. Midwives and neonatal nurses need to ensure that they emphasise and support the relational aspects of parenting and avoid over-emphasising milk intake and associated progress of the infant

"We sold a million units": the role of advertising past-sales

In a market where past-sales embed information about consumers’ tastes (quality), we analyze the seller’s incentives to invest in a costly advertising campaign to report them under two informational assumptions. In the …rst scenario, a pooling equilibrium with past-sales advertising is derived. Information revelation only occurs when the seller bene…ciates from the herding behaviour that the advertising campaign induces on the part of consumers. In the second informational regime, a separating equilibrium with past-sales advertising is computed. Information revelation always happens, either through prices or through costly advertisements.

Geographical externalities and the Pacifying Police Units Program in Rio de Janeiro

The paper quantifies the effects on violence and police activity of the Pacifying Police Unit program (UPP) in Rio de Janeiro and the possible geographical spillovers caused by this policy. This program consists of taking selected shantytowns controlled by criminals organizations back to the State. The strategy of the policy is to dislodge the criminals and then settle a permanent community-oriented police station in the slum. The installation of police units in these slums can generate geographical spillover effects to other regions of the State of Rio de Janeiro. We use the interrupted time series approach proposed by Gonzalez-Navarro (2013) to address effects of a police when there is contagion of the control group and we find that criminal outcomes decrease in areas of UPP and in areas near treated regions. Furthermore, we build a model which allows to perform counterfactuals of this policy and to estimate causal effects in other areas of the State of Rio de Janeiro outside the city.

Avaliação de produtos naturais no controle de biofilmes formados em sistema dinâmico

The biofilms microbial forms of association are responsible for generating, accelerating and / or induce the process of corrosion. The damage generated in the petroleum industry for this type of corrosion is significatives, representing major investment for your control. The aim of this study was to evaluate such tests antibiograms the effects of extracts of Jatropha curcas and essential oil of Lippia gracilis Schauer on microrganisms isolated from water samples and, thereafter, select the most effective natural product for further evaluation of biofilms formed in dynamic system. Extracts of J. curcas were not efficient on the complete inhibition of microbial growth in tests type antibiogram, and essential oil of L. gracilis Schauer most effective and determined for the other tests. A standard concentration of essential oil of 20 μL was chosen and established for the evaluation of the biofilms and the rate of corrosion. The biocide effect was determined by microbial counts of five types of microorganisms: aerobic bacteria, precipitating iron, total anaerobic, sulphate reducers (BRS) and fungi. The rate of corrosion was measured by loss of mass. Molecular identification and scanning electron microscopy (SEM) were performed. The data showed reduction to zero of the most probable number (MPN) of bacteria precipitating iron and BRS from 115 and 113 minutes of contact, respectively. There was also inhibited in fungi, reducing to zero the rate of colony-forming units (CFU) from 74 minutes of exposure. However, for aerobic and anaerobic bacteria there was no significant difference in the time of exposure to the essential oil, remaining constant. The rate of corrosion was also influenced by the presence of oil. The essential oil of L. gracilis was shown to be potentially effective

Beleza e poder na Ginástica Rítmica: reflexões para a educação física

La beauté dans la Gymnastique Rythmique (GR) s est esquissée comme condition de son existence. Pour son analyse, nous avons eu recourt au discours sur le pouvoir de Foucault (1971, 1979, 1987, 1988, 1997, 2003) et à sa relation avec la production de savoirs. Basés sur cette compréhension, nous avons réfléchi sur les relations de pouvoir dans la GR qui se sont établies et consolidées grâce à la réglementation de sa pratique, dans lequel le Code de Pointage a un rôle prépondérant. Ainsi, la GR a construit sa beauté à travers les temps au moyen de jeux de force où la gestualité de corps performatiques, à travers la discipline, a été prépondérant. Cette dernière a configuré des sens attelés à la coercition-résistence des corps: la production de discours. C est en pensant à une beauté comme ume trame de discours construits par ces relations de pouvoir-savoir des investissements du corps dans la Gymanstique Rythmique que nous nous posons les questions: Comment le Code de Pointage réglemente la gymanstique rythmique et sportive au sujet de la construction de la beauté ? Quelle est la relation entre les pouvoirs et les savoirs impliqués dans cette réglementation ? Nous avons donc pour objectifs de rechercher la beauté dans la Gymnastique Rythmique comme savoir produit à partir des relations du pouvoir circonscrites dans les règles de la modalité et de discuter la beauté à partir de la relation pouvoir/savoir comme réflexion pour le milieu de l éducation physique. Nous avons utilisé comme méthodologie la technique de l analyse de contenu (Bardin, 1977) afin d analyser le Code de Pointage de la GR dans sa version 2005-2008. Nous avons également fait usage des images de gymnastes comme moyen analogique pour amplifier le sens des discussions. La lecture fluctuante nous a permis de sélectionner des unités significatives et d organiser nos discussions en trois axes thématiques qui composent le premier chapitre intitulé « La beauté réglementée ». Dans ce chapitre, nous discutons les spécificités de la GR, la prescription de l utilisation du temps et de l espace et la configuration du geste technique à partir de l analyse de son code de ponctuation. Dans le deuxième chapitre, « Le corps beau transcende la règle », nous réalisons quelques réflexions destinées à l éducation physique à partir de la discussion du chapitre antérieur en prenant pour cible trois sujets : Pouvoirs et Savoirs, Technique et Style, Beauté et Éducation. Nous avons ainsi constaté que la beauté de la Gymnastique Rythmique contemporaine est entourée par sa réglementation, mais a été et continue à être dessinée par des mécanismes de pouvoir-savoir tout au long de sa trajectoire historique. Malgré l existence de conditions pour la beauté dans le Code de Pointage de la GR, il existe la possibilité de la création du propre style par la gymnaste, par la possibilité de vivre l improvisé et l imprévu, de sensibiliser le public, parce que le pouvoir crée des savoirs et le corps, qui se dépasse, créera toujours de nouvelles formes d être beau. La constatation que le Code de Pointage produit une beauté et que la gymnaste la reconstruit continuellement en en réactualisant les règles est une réflexion importante pour l éducation physique: elle réaffirme que le corps n est jamais seulement soumis, que même dans la soumission il est capable de produir du savoir, d être beau et de créer de nouveaux sens pour la Culture de Mouvements