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.

Polynomial identities for the ternary cyclic sum

We simplify the results of Bremner and Hentzel [J. Algebra 231 (2000) 387-405] on polynomial identities of degree 9 in two variables satisfied by the ternary cyclic sum [a, b, c] abc + bca + cab in every totally associative ternary algebra. We also obtain new identities of degree 9 in three variables which do not follow from the identities in two variables. Our results depend on (i) the LLL algorithm for lattice basis reduction, and (ii) linearization operators in the group algebra of the symmetric group which permit efficient computation of the representation matrices for a non-linear identity. Our computational methods can be applied to polynomial identities for other algebraic structures.

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.

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.

On Groups Whose Maximal Cyclic Subgroups Are Maximal

We consider the problem of classifying those groups whose maximal cyclic subgroups are maximal. We give a complete classification of those groups with this property and which are either soluble or residually finite.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

Crystalline particles from self-assembled divinyl oligomers

Ethylene glycol dimethacrylate (EGDMA) and/or triethylene glycol dimethacrylate (TEGDMA) oligomers formation was catalyzed in aqueous medium by horseradish peroxidase (HRP) in the presence of H(2)O(2) at room temperature. EGDMA and/or TEGDMA oligomers were characterized by means of gel permeation chromatography, infrared vibrational spectroscopy and (1)H NMR spectroscopy. Self-assembling of oligomers led to right-angled crystalline particles, as evidenced by scanning electron microscopy and differential scanning calorimetry. EGDMA, TEGDMA and EGDMA-co-TEGDMA oligomers synthesized in the presence of HRP-H(2)O(2) system presented pendant vinyl groups along the chains. good solubility in chloroform, and well-defined melting point. These features evidenced few cross-linking or cyclization and revealed that the catalytic properties of HRP led to oligomeric materials with new characteristics. (C) 2008 Elsevier B.V. All rights reserved.

Stereoselective Nucleophilic Addition of Potassium Alkyltrifluoroborates to Cyclic N-Acyliminium Ions: a Simple and Mild Approach to Chiral 5-Alkyl-pyrrolidin-2-ones

The stereoselective nucleophilic addition of potassium alkyltrifluoroborates to cyclic N-acyliminium ions derived from N-benzyl-3,4,5-triacetoxy-pyrrolidin-2-one, which affords 5-substituted-pyrrolidin-2-ones, is described. The products are obtained in moderate to good yields and are produced predominantly as the anti diastereomer.

Synthesis and spectroscopic characterization of polymer and oligomers of ortho-phenylenediamine

Poly(ortho-phenylenediamine) and oligomers of ortho-phenylenediamine were chemically synthesized and characterized by UV-vis, (1)H and (13)C NMR, FTIR and resonance Raman spectroscopies. Polymerization of ortho-phenylenediamine in HCl medium with ammonium persulfate only leads the trimer compound, in disagreement with some previous reports. Nevertheless, in acetic acid medium it was possible to prepare a polymer constituted by ladder phenazinic segments with different protonation levels and quinonediimine rings (polyaniline-like). X-ray absorption at N K-edge (N K XANES), X-ray photoelectron (XPS) and Electron paramagnetic resonance (EPR) spectroscopies were used to determine the different kinds of nitrogen presents in this class of polymer. N K XANES spectrum of poly(ortho-phenylenediamine) shows the band of -N=nitrogen of non-protonated phenazinic rings at 398.2 eV. In addition, XPS and N K XANES data confirm the presence of different types of protonated nitrogens in the polymeric poly(ortho-phenylenediamine) chain and the EPR spectrum shows that the polymer has a very weak polaronic signal. (C) 2009 Elsevier Ltd. All rights reserved.

Phenol-furfural resins to elaborate composites, reinforced with sisal fibers - Molecular analysis of resin and properties of composites

Resol type resins were prepared in alkaline conditions (potassium hydroxide or potassium carbonate) using furfural obtained by acid hydrolysis of abundant renewable resources from agricultural and forestry waste residues. The structures of the resins were fully determined by H-1, C-13, and 2D NMR spectrometries with the help of four models compounds synthesized specially for this study. MALDI-Tof mass spectrometry experiments indicated that a majority of linear oligomers and a minority of cyclic ones constituted them. Composites were prepared with furfural-phenol resins and sisal fibers. These fibers were chosen mainly because they came from natural lignocellulosic material and they presented excellent mechanical microscopy images indicated that the composites displayed excellent adhesion between resin and fibers. Impact strength measurement showed that mild conditions were more suitable to prepare thermosets. Nevertheless, mild conditions induced a high-diffusion coefficient for water absorption by composites. Composites with good properties could be prepared using high proportion of materials obtained from biomass without formaldehyde. (c) 2008 Wiley Periodicals, Inc.

Deposition of selenium thin layers on gold surfaces from sulphuric acid media: Studies using electrochemical quartz crystal microbalance, cyclic voltammetry and AFM

In this paper we report here new considerations about the relationship between the mass and charge variations (m/z relationship) in underpotential deposition (UPD), bulk deposition and also in the H(2)Se formation reaction. Nanogravimetric experiments were able to show the adsorption of H(2)SeO(3) on the AuO surface prior to the voltammetric sweep and that, after the AuO reduction, 0.40 monolayer of H(2)SeO(3) remains adsorbed on the newly reduced Au surface, which was enough to gives rise to the UPD layer. The UPD results indicate that the maximum coverage with Se(ads) on polycrystalline gold surface corresponds to approximately 0.40 monolayer, in good agreement with charge density results. The cyclic voltammetry experiments demonstrated that the amount of bulk Se obtained during the potential scan to approximately 2 Se monolayers, which was further confirmed by electrochemical quartz crystal microbalance (EQCM) measurements that pointed out a mass variation corresponding of 3 monolayers of Se. In addition, the Se thin films were obtained by chronoamperometric experiments, where the Au electrode was polarized at +0.10V during different times in 1.0 M H(2)SO(4) + 1.0 mM SeO(2). The topologic aspects of the electrodeposits were observed in Atomic Force Microscope (AFM) measurements. Finally, in highly negative potential polarizations, the H(2)Se formation was analyzed by voltammetric and nanogravimetric measurements. These finding brings a new light on the selenium electrodeposition and point up to a proposed electrochemical model for molecule controlled surface engineering. (c) 2009 Elsevier Ltd. All rights reserved.

Epichlorohydrin Cross-Linking of Synthetic DNA Oligomers

Epichlorohydrin (ECH), an important chemical in the synthetic polymer industry, is a bifunctional alkylating agent with the potential to form DNA interstrand crosslinks. Occupational exposure to this suspect carcinogen leads to chromosomal aberrations, and ECH has been shown to undergo reaction with DNA in vivo and in vitro. We are using denaturing polyacrylamide gel electrophoresis to assess cross-linking of synthetic DNA oligomers by both ECH and the related compound, epibromohydrin (EBH). Both epihalohydrins produce a low-mobility band on denaturing gels consistent with an interstrand cross-link. Moreover, the efficiencies, sequence preferences, reaction kinetics, and pH dependence differ for the two compounds, suggesting different mechanisms of reaction. Understanding these alkylation reactions may help explain the role of the epihalohydrins in cancer development.

Determination of Analgesics (Dipyrone and Acetaminophen) in Pharmaceutical Preparations by Cyclic Voltammetry at a Copper(II) Hexacyanoferrate(III) Modified Carbon Paste Electrode

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)