Some results on supersolvability of finite groups

We get new characterizations of finite supersolvable groups based on the structure of the generalized Fitting subgroup. Then we extend our results to the saturated formations containing the class of all supersolvable groups. Authors’ addresses: M. Asaad, Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt; Piroska Cs?rg?, Department of Algebra and Number Theory, E?tv?s University, Pázmány Péter sétány 1/c, H-1117 Budapest, Hungary     

Finite groups with given nearly s-embedded subgroups

Let G be a finite group and H a subgroup of G. We say that H is s-permutable in G if HP = PH for all Sylow subgroups P of G; H is s-semipermutable in G if HP = PH for all Sylow subgroups P of G with (|P|, |H|) = 1. Let H _s G be the subgroup of H generated by all those subgroups of G which are s-permutable in G and H ^sG the intersection of all such s-permutable subgroups of G contain H. We say that H is nearly s-embedded in G if G has an s-permutable subgroup T such that H ^sG = HT and \({H \cap T \leqq H_{ssG}}\) , where H _ssG is an s-semipermutable subgroup of G contained in H. In this paper, we study the structure of a finite group G under the assumption that some subgroups of prime power order are nearly s-embedded in G. A series of known results are improved and extended.     

Infrared and Raman spectra, conformational stability and vibrational assignment of 1-chloro-1-silacyclopentane

Infrared and Raman spectra (3500-60 cm⁻¹) of gas and/or liquid and solid 1-chloro-1-silacyclopentane (c-C₄H₈SiClH) have been recorded and the vibrational data indicate the presence of a single conformer with no symmetry which is consistent with the twisted form. Ab initio calculations with a variety of basis sets up to MP2(full)/aug-cc-pVTZ predict the envelope-axial and envelope-equatorial conformers are saddle points with nearly the same energies but much lower in energy than the planar conformer. Density functional theory calculations by the B3LYP method predicts slightly lower energies for the two envelope forms and considerably lower for the planar form. By utilizing the MP2(full)/6-31G(d) calculations the force constants, frequencies, infrared intensities, band contours, Raman activities, and depolarization values have been obtained to support the vibrational assignment. Estimated r₀ structural parameters have been obtained from adjusted MP2(full)/6-311 + G(d, p) calculations. These experimental and theoretical results are compared to the corresponding quantities of some other five-membered rings.     

Das KLL-Auger-Spektrum für 10≦Z≦36

The configuration interaction, applied very recently byAsaad to the calculations ofKLL-Auger spectra, could remove the large discrepancies which existed for lowZ between experimental and theoretical relative group intensities I(KL₁L_2,3)/I(KL₁L₁) and I(KL_2,3L_2,3)/I(KL₁L₁).Asaad's calculations, however, were based on binding energies E(L₁) and energies of the Coulomb and spin-orbit interaction, which were not very accurate. In the present calculations use has been made of more accurate binding energies E(L₁) and Coulomb and spin-orbit interaction energies. It is shown that the absolute error in the results of the new calculations is less than 10%. From this it follows that the remaining discrepancies between theoretical and experimental values of the group intensities for 10≦Z<25 may be solely attributed to the inadequacy of the calculated transition probabilities. This calls for calculations of transition amplitudes of the KLL-process with more accurate wave functions for Z<25, in particular for Z=10.     

TheL 2 MM andL 3 MM spectra of argon

Expressions for the line intensities in theL ₂ MM andL ₃ MM spectra of elements of lowZ are given. For such elements the inner shell vacancy is given inj-j notation whereas the final double vacancy in the outer shell is given in Russell-Saunders coupling. Line intensities in theL ₂ MM andL ₃ MM spectra of argon are calculated using the transition amplitudes computed byRubenstein. No configuration interaction is considered.     

Preorganization in highly enantioselective diaza-Cope rearrangement reaction

Crystal structure and activation entropy data indicate that H-bond directed diaza-Cope rearrangement of chiral diimines takes place with a high degree of preorganization. CD spectroscopy and HPLC data show that there is inversion of stereochemistry for the reaction with excellent enantioselectivity.     

Racemisation in Chemistry and Biology

The two enantiomers of a compound often have profoundly different biological properties and thus their liability to racemisation in aqueous solutions is an important piece of information. The authors reviewed the available data concerning the process of racemisation in vivo, in the presence of biological molecules (e.g., racemase enzymes, serum albumin, cofactors and derivatives) and under purely chemical but aqueous conditions (acid, base and other aqueous systems). Mechanistic studies are described critically in light of reported kinetic data. The types of experimental measurement that can be used to effectively determine rate constants of racemisation in various conditions are discussed and the data they provide is summarised. The proposed origins of enzymatic racemisation are presented and suggest ways to promote the process that are different from processes taking place in bulk water. Experimental and computational studies that provide understanding and quantitative predictions of racemisation risk are also presented.     

Quantitative Prediction of Rate Constants for Aqueous Racemization To Avoid Pointless Stereoselective Syntheses

Racemization has a large impact upon the biological properties of molecules but the chemical scope of compounds with known rate constants for racemization in aqueous conditions was hitherto limited. To address this remarkable blind spot, we have measured the kinetics for racemization of 28 compounds using circular dichroism and ¹H NMR spectroscopy. We show that rate constants for racemization (measured by ourselves and others) correlate well with deprotonation energies from quantum mechanical (QM) and group contribution calculations. Such calculations thus provide predictions of the second‐order rate constants for general‐base‐catalyzed racemization that are usefully accurate. When applied to recent publications describing the stereoselective synthesis of compounds of purported biological value, the calculations reveal that racemization would be sufficiently fast to render these expensive syntheses pointless.