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.

Conformational Properties of Angiotensin II and Its Active and Inactive TOAC-Labeled Analogs in the Presence of Micelles. Electron Paramagnetic Resonance, Fluorescence, and Circular Dichroism Studies

The interaction between angiotensin II (AII, DRVYIHPF) and its analogs carrying 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid (TOAC) and detergents-negatively charged sodium dodecyl sulfate (SDS) and zwitterionic N-hexadecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate (HPS)-was examined by means of EPR, CD, and fluorescence. EPR spectra of partially active TOAC(1)-AII and inactive TOAC(3)-AII in aqueous solution indicated fast tumbling, the freedom of motion being greater at the N-terminus. Line broadening occurred upon interaction with micelles. Below SDS critical micelle concentration, broader lines indicated complex formation with tighter molecular packing than in micelles. Small changes in hyperfine splittings evinced TOAC location at the micelle-water interface. The interaction with anionic micelles was more effective than with zwitterionic micelles. Peptide-micelle interaction caused fluorescence increase. The TOAC-promoted intramolecular fluorescence quenching was more, pronounced for TOAC(3)-AII because of the proximity between the nitroxide and Tyr(4). CD spectra showed that although both AII and TOAC(1)-AII presented flexible conformations in water, TOAC(3)-AII displayed conformational restriction because of the TOAC-imposed bend (Schreier et al., Biopolymers 2004, 74, 389). In HPS, conformational changes were observed for the labeled peptides at neutral and basic pH. In SDS, all peptides underwent pH-dependent conformational changes. Although the spectra suggested similar folds for All and TOAC(1)-AII, different conformations were acquired by TOAC(3)-AII. The membrane environment has been hypothesized to shift conformational equilibria so as to stabilize the receptor-bound conformation of ligands. The fact that TOAC(3)-AII is unable to acquire conformations similar to those of native AII and partially active TOAC(1)-AII is probably the explanation for its lack of biological activity. (C) 2009 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 92: 525-537, 2009.

Experimental Evidence of the Occurrence of Intramolecular Electron Transfer in Catalyzed 1,2-Dioxetane Decomposition

The activation parameters for the thermal decomposition of 13 acridinium-substituted 1,2-dioxetanes, bearing an aromatic moiety, were determined and their chemiluminescence emission quantum yields estimated, utilizing in situ photosensitized 1,2-dioxetane generation and observation of its thermal decomposition kinetics, without isolation of these highly unstable cyclic peroxides. Decomposition rate constants show linear free-energy correlation for electron-withdrawing substituents, with a Hammett reaction constant of rho = 1.3 +/- 0.1, indicating the occurrence of an intramolecular electron transfer from the acridinium moiety to the 1,2-dioxetane ring, as postulated by the intramolecular chemically initiated electron exchange luminescence (CIEEL) mechanism. Emission quantum yield behavior can also be rationalized on the basis of the intramolecular CIEEL mechanism, additionally evidencing its occurrence in this transformation. Both relations constitute the first experimental evidence for the occurrence of the postulated intramolecular electron transfer in the catalyzed and induced decomposition of properly substituted 1,2-dioxetanes.

Polyaniline/layered zirconium phosphate nanocomposites: Secondary-like doped polyaniline obtained by the layer-by-layer technique

In the present work, nanocomposites of polyaniline (PANI) and layered alpha-Zr(HPO4)(2).H2O (alpha-ZrP) were prepared using two different approaches: (i) the in situ aniline polymerization in the presence of the layered inorganic material and (ii) the layer-by-layer (LBL) assembly using an aqueous solution of the polycation emeraldine salt (ES-PANI) and a dispersion of exfoliated negative slabs of alpha-ZrP. These materials were characterized spectroscopically using mainly resonance Raman scattering at four exciting radiations and electronic absorption in the UV-VIS-NIR region. Structural and textural characterizations were carried out using powder X-ray diffraction (XRD) and scanning electron microscopy (SEM). The polymer obtained by the in situ aniline polymerization is located primarily in the external surface of the inorganic material although aniline monomers were intercalated between alpha-ZrP interlayer regions before oxidative polymerization. Through resonance Raman spectroscopy, it was observed that the formed polymer has semiquinone units (ES-PANI) and also azo bonds (-N = N-), showing that this method results in a polymer with a different structure from the usual ""head-to-tail"" ES-PANI. The LBL assembly of pre-formed ES-PANI and exfoliated alpha-ZrP particles produces homogeneous films with reproducible deposition from layer to layer, up to 20 bilayers. Resonance Raman (lambda(0) = 632.8 nm) spectrum of PANI/ZrP LBL film shows an enhancement in the intensity of the polaronic band at 1333 cm(-1) (nu C-N center dot+) and the decrease of the band intensity at 1485 cm(-1) compared to bulk ES-PANI. Its UV-VIS-NIR spectrum presents an absorption tail in the NIR region assigned to delocalized free charge carrier. These spectroscopic features are characteristic of highly conductive secondary doped PANI suggesting that polymeric chains in PANI/ZrP LBL film have a more extended conformation than in bulk ES-PANI.

Oxidation of anilinium ions intercalated in montmorillonite clay by electrochemical route

Resonance Raman, FTIR, X-ray diffraction, UV-vis-NIR, electron paramagnetic resonance, X-ray absorption at Si K-edge and electron microscopy were employed for characterizing the products formed through electrochemical oxidation of intercalated anilinium ions inside the cationic montmorillonite (MMT) clay. The layer silicate structure was not affected by the anilinium oxidation between the layers. The intercalated products present only an electronic absorption band at 400 nm, very low conductivity (ca. 10(-7) S cm(-1)) and their Raman spectrum displays bands, with high relative intensities, assigned to the benzidine dication, indicating that this product was formed in high amount. Nevertheless, bands that can be correlated to phenazine-like segments and 1,4-phenylenediamine repeat units (PANI like segments) are also observed. The very low EPR signal indicates that diamagnetic species are predominant. All results are compared to those obtained by anilinium-MMT chemically oxidized by persulfate and the differences are pointed out. (C) 2008 Elsevier B.V. All rights reserved.

In situ generation of n-butanethiol and its reaction with electron-deficient olefines

n-Butanethiol is generated in situ by sequential addition of n-butyllithium and water to elemental sulfur. The n-butanethiol formed was reacted with electron-deficient olefines to give Michael-type addition products in good yields. The method avoids the manipulation of the bad-smelling n-butanethiol.

Interfacial Electron Transfer Dynamics Following Laser Flash Photolysis of [Ru(bpy)(2)((4,4 `-PO(3)H(2))(2)bpy)](2+) in TiO(2) Nanoparticle Films in Aqueous Environments

Nanosecond laser flash photolysis has been used to investigate injection and back electron transfer from the complex [(Ru-(bpy)(2)(4,4`-(PO(3)H(2))(2)bpy)](2+) surface-bound to TiO(2) (TiO(2)-Ru(II)). The measurements were conducted under conditions appropriate for water oxidation catalysis by known single-site water oxidation catalysts. Systematic variations in average lifetimes for back electron transfer, - were observed with changes in pH, surface coverage, incident excitation intensity, and applied bias. The results were qualitatively consistent with a model involving rate-limiting thermal activation of injected electrons from trap sites to the conduction band or shallow trap sites followed by site-to-site hopping and interfacial electron transfer, TiO(2)(e(-))-Ru(3+) -> TiO(2)-Ru(2+). The appearance of pH-dependent decreases in the efficiency of formation of TiO(2)-Ru(3+) and in incident-photon-to-current efficiencies with the added reductive scavenger hydroquinone point to pH-dependent back electron transfer processes on both the sub-nanosecond and millisecond-microsecond time scales, which could be significant in limiting long-term storage of multiple redox equivalents.