The congruence subgroup problem for branch groups

We state and study the congruence subgroup problem for groups acting on rooted trees, and for branch groups in particular. The problem is reduced to the computation of the congruence kernel, which we split into two parts: the branch kernel and the rigid kernel. In the case of regular branch groups, we prove that the first one is abelian while the second has finite exponent. We also establish some rigidity results concerning these kernels.     

Estimation of the Dynamics of the Drift of Spectral Lines and Computer Correction of the Scan of a Mass Spectrum

This article describes the technique used to estimate the temporal positions of spectral lines of a quadrupole mass spectrometer and to automatically determine mass numbers without resorting to reference substances, as well as the algorithms of digital registration of mass spectra and the technical means of an experimental automated system based on a serial MX-7304A mass spectrometer and a personal computer. The results of experimental investigations of the dynamics of the drift of peaks and the results of tests of the technique under real conditions are given. The error in determining the atomic mass unit (u) by the technique developed was not higher than 0.01%.     

Linear groups

This survey article covers papers abstracted inReferativnyi Zhurnal Matematika during the period 1978–1982 and is a continuation of the surveys Linear groups published in 1967, 1971, and 1977 in the seriesAlgebra, Topology, Geometry (Itogi Nauki i Tekhniki). The main things under consideration are linear groups over rings and the structure of infinite linear groups. Some very recent results are also mentioned.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 21, pp. 135–182, 1983.     

Minimal characters of the finite classical groups

Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we deter-mine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r r a prime divisor of the group order.     

Feasibility of the solar-pumped fullerene-oxygen-iodine laser (Sun-light FOIL)

The feasibility of the optically pumped (in particular, solar-pumped) fullerene-oxygen-iodine laser (FOIL) is considered. The singlet oxygen is assumed to be formed through the interaction of molecular oxygen with a mixture of (both lower and higher) fullerenes in a photogenerated triplet metastable state. The estimates based on a photokinetic model show that the solar-pumped FOIL efficiency can reach several tens of percent. The singlet-oxygen yield resulting from the interaction of optical pumping radiation with fullerenes in solutions is studied both theoretically and experimentally. As the optical pumping, we used laser radiation at 532 nm and broad-band emission of a lamp with a solarlike spectrum.     

An example of a torsion-free nilpotent group having no outer automorphisms

A negative answer is given to a question posed by E. Schenkman and F. Haimo: does every torsion-free nilpotent group have an outer automorphism?     

The reaction of pentachloropyridine with aliphatic amines

The reaction of pentachloropyridine with aliphatic amines has given a series of 2-alkylaminotetrachloropyr idines.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 6, No. 7,pp. 959–962, July, 1970.