The Schur property for subgroup lattices of groups

A classical theorem of Schur states that if the centre of a group G has finite index, then the commutator subgroup G′ of G is finite. A lattice analogue of this result is proved in this paper: if a group G contains a modularly embedded subgroup of finite index, then there exists a finite normal subgroup N of G such that G/N has modular subgroup lattice. Here a subgroup M of a group G is said to be modularly embedded in G if the lattice is modular for each element x of G. Some consequences of this theorem are also obtained; in particular, the behaviour of groups covered by finitely many subgroups with modular subgroup lattice is described. Received: 16 October 2007, Final version received: 22 February 2008     

A dilute-and-inject low-pressure gas chromatography-tandem mass spectrometry method for phthalate determination in extra virgin olive oil

The goal of this study was to develop a method for the determination of nine phthalic acid esters in extra virgin olive oils using low-pressure gas chromatography-triple-quadrupole mass spectrometry. Sample preparation was simple, environmental friendly, and rapid inasmuch that it involved only dilution (< 1 mL of hexane). The low-pressure gas chromatography analyses were performed by using a 5 m wide-bore column. The limit of quantification for the phthalates ranged from 0.06 to 1.14 mg kg⁻¹. Both intra- and interday precisions were measured, with coefficient of variation values ranging from 0.2% to 11.7%. The trueness of the method was measured by evaluating accuracy at the initial stage of the work and after 2 months, with values ranging between −8.7% and 12.1%. Moreover, blind accuracy was comprised between −11.6% and 14.2%. The method involves the use of simplified instrumentation and reduced analysis times (nearly two times faster) compared to a previously published comprehensive two-dimensional gas chromatography-triple-quadrupole mass spectrometry method, leading to a reduction of energy and helium consumption. The approaches were compared in analytical terms and for the environmental impact. In total, 23 olive oil samples were analyzed, with at least one phthalate detected in all but one sample.     

Synthesis, molecular structure and properties of the [H6-nNi30C4(CO)34(CdCl)2]n- (n=3-6) bimetallic carbide carbonyl cluster: a model for the growth of noncompact interstitial metal carbides

Reaction of the [Ni(9)C(CO)(17)](2-) dianion with CdCl(2)2.5 H(2)O in THF affords the novel bimetallic Ni--Cd carbide carbonyl clusters [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) (n=3-6), which undergo several protonation-deprotonation equilibria in solution depending on the basicity of the solvent or upon addition of acids or bases. Although the occurrence in solution of these equilibria complicates the pertinent electrochemical studies on their electron-transfer activity, they clearly indicate that the clusters [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) (n=3-6), as well as the structurally related [H(6-n)Ni(34)C(4)(CO)(38)](n-) (n=4-6), undergo reversible or partially reversible redox processes and provide circumstantial and unambiguous evidence for the presence of hydrides for n=3, 4 and 5. Three of the [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-) anions (n=4-6) have been structurally characterized in their [NMe(3)(CH(2)Ph)](4)[H(2)Ni(30)C(4)(CO)(34)(CdCl)(2)]2 COMe(2), [NEt(4)](5)[HNi(30)C(4)(CO)(34)(CdCl)(2)]2 MeCN and [NMe(4)](6)[Ni(30)C(4)(CO)(34)(CdCl)(2)]6 MeCN salts, respectively. All three anions display almost identical geometries and bonding parameters, probably because charge effects are minimized by delocalization over such a large metal carbonyl anion. Moreover, the Ni(30)C(4) core in these Ni-Cd carbide clusters is identical within experimental error to those present in the [HNi(34)C(4)(CO)(38)](5-) and [Ni(35)C(4)(CO)(39)](6-) species, suggesting that the stepwise assembly of their nickel carbide cores may represent a general pathway of growth of nickel polycarbide clusters. The fact that the [H(6-n)Ni(30)C(4)(CO)(34)(micro(5)-CdCl)(2)](n-)(n=4-6) anions display two valence electrons more than the structurally related [H(6-n)Ni(34)C(4)(CO)(38)](n-) (n=4-6) species has been rationalized by extended Hückel molecular orbital (EHMO) analysis.     

Rapid access to 1,6-anhydro-beta-L-hexopyranose derivatives via domino reaction: synthesis of L-allose and L-glucose

An expeditious and efficient synthesis of 1,6-anhydro-beta-L-hexopyranosyl derivatives 3 as valuable building blocks for the preparation of L-sugars is herein reported. This route relies upon the use of a domino reaction involving five synthetic steps from the 5,6-dihydro-1,4-dithiin 4. As 1,6-anhydro derivatives 3 are obtained, dithioethylene bridge removal and double-bond dihydroxylation give access to protected L-allose and L-glucose in stereoselective fashion and high yields.     

Rendering a calixarene having dipyridyl pendants soluble in water results in different species with smaller binding constants

Sulfonato groups were introduced into the backbone of a dipyridyl-based calixarene to obtain a novel water-soluble compound able to complex Co(II) and Cu(II). Spectrophotometric titrations pointed out that the new ligand complexes Co(II) and Cu(II) in water, but with stoichiometries and stabilities that are different from the analogous water insoluble calixarene.     

Comprehensive two-dimensional liquid chromatography-based quali-quantitative screening of aqueous phases from pyrolysis bio-oils

Pyrolysis processes are an alternative to minimize the environmental problem associated to agrifood industrial wastes. The main product resulting from these processes is a high-value liquid product, called bio-oil. Recently, the use of comprehensive two-dimensional liquid chromatography (LC × LC) has been demonstrated as a useful tool to improve the characterization of the water-soluble phases of bio-oils, considering their complexity and high water content. However, the precise composition of bio-oils from different agrifood byproducts is still unknown. In the present study, the qualitative and quantitative screening of eight aqueous phases from different biomasses, not yet reported in the literature, using LC × LC is presented. The two-dimensional approach was based on the use of two reverse phase separations. An amide column in the first dimension together with a C18 column in the second dimension were employed. Thanks to the use of diode array and mass spectrometry detection, 28 compounds were identified and quantified in the aqueous phase samples with good figures of merit. Samples showed a distinct quali-quantitative composition and a great predominance of compounds belonging to aldehydes, ketones and phenols, most of them with high polarity.     

Novel ethylene/norbornene copolymers as nonreleasing antioxidants for food‐contact polyolefinic materials

An efficient procedure for the copolymerization of ethylene (E) with a novel norbornenic comonomer (N_ArOH) bearing a stabilizing moiety analogous to commercial antioxidant 2,6‐di‐tert‐butyl‐4‐methylphenol (BHT) is successfully developed. This study is aimed at: i) tuning the concentration of the stabilizing function along the polymer chain, and ii) preparing “nonreleasing” polymeric additives specifically destined to protect commercial low‐density polyethylene (LDPE). Films obtained from blends of the novel E/N_ArOH copolymers with an antioxidant‐free LDPE matrix are characterized by superior thermal, thermo‐oxidative, and photostability when compared not only with neat LDPE films but also with films stabilized by the commercial BHT additive. Specific migration tests conducted in order to investigate the nonreleasing character of the novel macromolecular additives confirm the reduced risk of migration, from the films into food simulants, of unreacted comonomer or degradation products bearing the antioxidant moiety. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013 , 51, 1007–1016     

Polycyclic groups with modular finite homomorphic images

A group G is said to be a modular group if it has modular subgroup lattice. We will prove in this paper that a polycyclic group G is modular if and only if all its finite homomorphic images are modular groups. Similar results will also be obtained for other conditions of modular type.