A note on a theorem of W. Gaschütz and N. Itô

Given a finite groupG andp an odd prime number, we conclude thatO ^p(G)G isp-nilpotent when for every subgroupH ofG of orderp there exists a subgroupK ofG such thatG=HK andH permutes with every subgroup ofK.     

Arcs in the Hall Planes

Using a transformation tecnique for designs introduced in [1], I construct a class of arcs embeddeable in the Hall plane and in the dual of the Hall plane of order q proving also their completeness in the unital of Grüning. Math. Subj. Class.: 51A35 Non Desarguesian affine and projective planes. 51E22 Blocking sets, ovals, k-arcs.     

Ab initio molecular dynamics simulation of a room temperature ionic liquid

Ab initio molecular dynamics simulations have been performed for the first time on the room-temperature organic ionic liquid dimethyl imidazolium chloride [DMIM][Cl] using density functional theory. The aim is to compare the local liquid structure with both that obtained from two different classical force fields and from neutron scattering experiments. The local structure around the cation shows significant differences compared to both the classical calculations and the neutron results. In particular, and unlike in the gas-phase ion pair, chloride ions tend to be located near a ring C-H proton in a position suggesting hydrogen bonding. The results are used to suggest ways in which the classical potentials may be improved.     

Cycloaddition reaction of 2-azadienes derived from beta-amino acids with electron-rich and electron-deficient alkenes and carbonyl compounds. Synthesis of pyridine and 1,3-oxazine derivatives

Functionalized keto-enamines 6 were obtained by nucleophilic addition of enol ethers to the imine moiety of 2-azadienes derived from dehydroaspartic esters 4. Reactions of 2-azadiene 4c containing three electron-withdrawing substituents (CO(2)R) with enol ethers 5 in the presence of lithium perchlorate led to the formation of tetrahydropyridine derivatives 7 in a regio- and stereoselective fashion. 2H-[1,3]-oxazines 10 and pyridine derivatives 12 and 13 were obtained by heterocycloaddition reactions of electron-poor azadienes 4d-g containing two electron-withdrawing substituents (4-O(2)N-C(6)H(4), CO(2)R) in positions 1 and 4 with carbonyl derivatives (ethyl glyoxalate 9a and diethyl ketomalonate 9b) and the electron-deficient olefin tetracyanoethylene 11.