Intersections of two nilpotent subgroups in finite groups with socle <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>(<Emphasis Type="Italic">q</Emphasis>)

Given a finite group G with socle isomorphic to L ₂(q), q ≥ 4, we describe, up to conjugacy, all pairs of nilpotent subgroups A and B of G such that A ∩ B ^g ≠ 1 for all g ∈ G.     

Finite groups in which the normalizers of pairwise intersections of Sylow 2-subgroups have odd indices

All finite semisimple groups are described in which the normalizers of pairwise intersections of Sylow 2-subgroups have odd indices; thereby, Problem 5.14(v) from the Kourovka Notebook is solved in the main.     

On intersections of solvable Hall subgroups in finite nonsolvable groups

The author continues the investigation of intersections of Hall subgroups in finite groups. Previously, the author proved that in the case when a Hall subgroup is Sylow there are three subgroups conjugate to it such that their intersection coincides with the maximal normal primary subgroup. A similar assertion holds for Hall subgroups in solvable groups. The aim of this paper is to construct examples of a (nonsolvable) group in which the intersection of any four subgroups conjugate to some Hall subgroup is nontrivial.     

Covers in the Lattice of Varieties of m-Groups

We consider some questions on covers in the lattice of varieties of m-groups. We prove the existence of a nonabelian cover of the smallest nontrivial variety of m-groups. We show that there exists an uncountable set of o-approximable varieties of m-groups each of which has continuum many o-approximable covers. In the lattice of o-approximable varieties of m-groups we find a variety that has no covers in this variety and no independent basis of identities.     

Photocatalytic Activity of Ruthenium(II) Complex with 1,10-Phenanthroline-3,8-dicarboxylic Acid in Aerobic Oxidation Reactions

Russian Journal of Organic Chemistry - Mixed-ligand ruthenium(II) complex with 2,2′-bipyridine and 1,10-phenanthroline-3,8-dicarboxylic acid with the composition...     

Dlab groups

We argue that for any subgroup H of rank 1 in a multiplicative group of positive reals, among Dlab groups of the closed intervalI=[0],[1] on an extended set of reals, there exist groups D_H*(I) and D_H* which lack normal relatively convex subgroups, are not simple groups, and have just two distinct linear orders. The cardinality of a set of linear orders on Dlab groups is computed. It is established that every rigid l-group is Abelian if it belongs to a varietyD of l-groups groups generated by the linearly ordered groups D_H*(I) and D_H*. We prove that the quasivariety q(D_H*(I), D_H*) of groups generated by D_H*(I) and D_H* is distinct from a quasivarietyO of all orderable groups. Similar results are stated for a variety of l-groups and the quasivariety of groups that are not embeddable in D_H*(I) and D_H*. Supported by RFFR grant No. 96-01-00088. Translated fromAlgebra i Logika, Vol. 38, No. 5, pp. 531–548, September–October, 1999.     

Charge-transfer transitions and optical properties of cobaltites

Specific features of the charge-transfer states and transitions of the O 2p → Co 3d type in octahedral complexes (CoO₆)^9? and (CoO₆)^10? are considered in the cluster approach. The reduced matrix elements of the electric dipole transition operator are calculated on the many-electron wave functions of the complexes corresponding to the initial (high-or low-spin) state and the final state at a charge-transfer transition. The energies of the many-electron charge-transfer transitions and their intensities are calculated within the Tanabe-Sugano theory taking into account the mixing of different configurations of the same symmetry. Simulation of the optical spectrum of cobaltites showed the presence of a wide band consisting of many lines due to the charge-transfer transitions. The results of the simulation are in agreement with experiment and demonstrate the limited validity of the generally accepted concepts of a simple structure of the spectrum of charge-transfer transitions.     

Charge-transfer transitions and optical spectra of vanadates

Specific features of the charge-transfer states and O2p → V3d transitions in the (VO₆)^9? octahedral complex are studied using the cluster approach. The reduced matrix elements of the electric-dipole transition operator are calculated for many-electron wave functions corresponding to the initial and final states of a charge-transfer transition. Using a parameterization of the results, the relative intensities of the allowed charge-transfer transitions are calculated disregarding the mixing of different configurations of the same symmetry. The Tanabe-Sugano theory is used with inclusion of this mixing to calculate the energies of many-electron charge-transfer transitions and their actual intensities. Modeling of the optical spectrum of LaVO₃ reveals a complicated charge-transfer transition band consisting of 81 lines. The main maxima of the band are in the range 6.3–7.3 eV. There are also additional maxima in the regions of ≈3 and ≈8–9 eV. The bandwidth is ≈10 eV. The results of model calculations are in agreement with experiments and demonstrate the weakness of the widely used assumption that the spectrum of charge-transfer transitions has a simple structure.